Sean Dyche has revealed Dominic Calvert-Lewin is back in training and will be assessed ahead of Saturday when Everton take on in-form Brentford at Goodison Park (3pm GMT).
The forward has missed the past five games after suffering a hamstring injury during the 1-0 home win over Arsenal last month. However, Dyche has confirmed Calvert-Lewin has been involved in full training this week and could return to the squad for Saturday's contest.
Left-back Vitalii Mykolenko could also be available for selection after overcoming the illness that saw him miss Sunday’s 2-2 draw away to Nottingham Forest, while right-back Nathan Patterson will be assessed after completing a full 90 minutes for the Under-21s in Monday’s Premier League 2 clash at home to Crystal Palace.
Andros Townsend (ACL) remains unavailable.
Asked about Calvert-Lewin's availability for this weekend in his pre-match press conference on Friday, Dyche said: "Dom is in and around it again, with us training. We are still making a decision on him being truly right to come back in.
"[On this weekend] it's early yet, he's just got on the grass with us, but he's done a lot of rehab - the stats and facts - and the way he's feeling is good. It's positive signs that's for sure."
On updates for Mykolenko, Patterson and Townsend, Dyche added: "Myko is just illness. We're making a decision on his strength. He is just coming out of illness but has trained today. Patto has played another game, but he's still just getting that true match sharpness.
"[Townsend] isn't close and he's had a knee injury with some setbacks. It seems to be calming now and he's in a better place with it now."
Sean Dyche says he has full belief in the ability of his squad and the clear signs of improvement during the early stages of his tenure as Everton manager ahead of Saturday's visit of Brentford.
Thomas Frank's in-form side head to Goodison Park on Saturday (3pm GMT) looking to extend their 12-game unbeaten run in the Premier League.
The Blues, meanwhile, begin the contest looking to build momentum following a strong performance and a point on the road at Nottingham Forest last weekend - and having won two of the first three home games since Dyche took charge in late January.
Dyche has been buoyed by the commitment and application of his players in that period and believes the Toffees are now "beginning to look more effective in different ways".
"I think [the Nottingham Forest game was] about building on the mentality that I've been speaking about since I've been here," he said. "That is the mentality to perform but also to take on whatever comes in front of you, with the way that we work and that's to have it tight enough defensively where we can affect games but also loose enough where we can affect it openly.
"I thought for large parts [of the Forest game], particularly in the first half, we were very good on both.
"Aside from a mistake and a soft one against Villa I thought it was a pretty thorough performance, to be honest. I thought we were good against Leeds.
"There are strong signs but signs don't give you anything. You don't just win because there are strong signs - you win because you get everything right throughout a 90-odd minute match.
"Like I've said before, all of us would take a lucky [result] now and again - anyone would - but you can't really build on lucky ones.
"You have to build on something that is real and I see something real that is happening. I see the team working effectively and efficiently. I see the shape getting better, working on transition better and we're beginning to find better ways of operating in the attacking third - more entries into the box, more quality entrances into the box. Now you add in the final details and the moment of truth when someone takes a chance.
"We're beginning to look more effective in different ways. We've never been wanting pure football all of the time. How many different ways can you affect the opposition? That's what I believe is correct about football and that's what we're trying to do."
Ahead of the visit of Brentford, Dyche revealed striker Dominic Calvert-Lewin has this week returned to training with the group, while Vitalii Mykolenko has also rejoined the group following illness and Nathan Patterson has been working on his fitness following another appearance for the Under-21s.
Demarai Gray was handed his first start under Dyche against Nottingham Forest and impressed with a busy shift in attack, as well as notching the opening goal via the penalty spot at the City Ground.
"I thought he did well," reflected Dyche. "We're asking to change a little bit. He worked hard and Neal Maupay has been working very hard as well. He's worked very hard in training this week - there's been no disappointment there - he has got on with it.
"I think Demarai showed signs of what he can do - he nicked a goal, albeit from the penalty spot but it's still another goal.
"I've enjoyed his open-mindedness to it because he has played there but it's not always that familiar to him.
"I think he delivered a good performance."
On the challenge Brentford will pose this weekend, Dyche believes the west London outfit have a "good mix" of different threats.
"They've done well," added Dyche. "They're proving that they're a good outfit and they're learning from last season into this season.
"I know the manager a little bit and I've spent a bit of time with him. I like what he's done. He's not a brand-est. He plays direct when they need to, they can play force football when they need to, they can play physically - but they can play as well.
"I think they've got a good mix there and it's another challenge right in front of us but, as I say, every team in the Premier League is there for a reason. Teams can have bad spells and things but there aren't 'bad teams', necessarily.
"Yet again, the method that we use to plan for these games is making sure all of the necessary information is giving to the players and that they understand the opposition, but then also what we can do to look after ourselves and get a result."