McInnes says he hopes Findlay and captain Lawrence Shankland, who has been missing since 17 January with a hamstring injury, will be back for the final pre-split game against Motherwell on 11 April.
Another key figure, midfielder Cammy Devlin, is due back in “two or three weeks” according to McInnes, as is defender Stephen Kingsley.
Hearts are four points clear of Rangers at the top of the Premiership.
“As it stands we had 11 players unavailable to train today, but we’ve still got enough to train and put a strong team out and a strong squad out on Saturday,” McInnes said.
“So my focus is the ones that are available, and just trying to get one or two who are in the 50-50 category available for the weekend.
“It’s easy to feel sorry for yourself, easy to think: ‘why us? why me?’ But it’s unrealistic to go through a full campaign [without injuries].
“It’s a league for as reason, you have to go through these different tests and challenges.
“There’s no doubt we’re getting challenged at the minute. Once we get through the next four games we will ideally be a bit stronger going into the final run in.
“It will almost feel like a transfer window opening up in April. So you’ve got to take the good with the bad.”
Midfielder McEntee went to see a specialist on Wednesday morning for a shoulder issue after a scan revealed “fairly positive” news.
Baningime has some bruising on his lower leg and McInnes says the midfielder is hopeful he can train on Friday and feature at Tynecastle against Aberdeen.
Kerjota, meanwhile, picked up a hip strain in a closed door friendly against Dundee on Tuesday but may well be fit to play too.