Centre-back Tarkowski was substituted as a precaution due to a tight hamstring during the closing stages of Saturday's 1-0 npower League One win over Portsmouth and was due to return to training on Monday alongside midfield duo Wesolowski (hamstring) and Winchester (ankle).
"We'll have to assess them and see how they are," said Philliskirk. "We'll probably know after the session if they're 100 per cent fit or if they're not.
"If they're not then they won't be considered because you can't go into a game against Everton without your players being 100 per cent fit. Fingers crossed, we're hopeful they'll all be okay."
Experienced defender Cliff Byrne overcame a groin complaint to take a place on the bench against Pompey and is expected to be involved once more.
Left-sided midfielders Cristian Montano (thigh) and Youssouf M'Changama (knee) remain on the sidelines, while playmaker Jose Baxter is set to return to Goodison Park in opposition for the first time.