The Owls have a number of players coming back from injury and Covid-19, and their only game since New Year's Day was the third-round win over Exeter City, where they were only able to name four substitutes.
They should be stronger now and will need to be against an Everton side whose form has put them on the heels of their city rivals Liverpool in the Premier League, but caretaker manager Thompson was playing his cards close to his chest.
Asked about the fitness of Massimo Luongo, Julian Borner, Chey Dunkley and Keiren Westwood after injury, he would only say that “not all of them” are available for selection after injury, but striker Jack Marriott, whose Hillsborough career had looked over, should be available at Goodison Park.
“We've had injury issues with them but they're coming along nicely,” he said of the quartet. “We'll check on them on Saturday in terms of availability for Sunday but they are progressing.
“We've had a couple back on the training pitch, which is quite nice, but we've got a lot of games coming up so we've got to be not ultra-careful but make sure it's the right time when we put them back in.
“With people just getting back in training after injury or otherwise we've got to treat everyone on their merits and make sensible decisions in terms of the long-term effect on that individual.
“We need to make sure we have as many players as possible available for the vast majority of games leading up to the end of the season.
“There's a couple (of other injuries) but I'm not going to give anything away. We'll wait and see.
“I don't want to say about injuries today knowing we've got tomorrow to think about.
“We've had a good training session and one or two of those who have had issues have been involved in that. We'll see how we come through that and make a decision based on that.”
Asked how strong a team he would put out for the evening kick-off, Thompson added: “It is a balancing act but I am a real believer in people playing football games. People love playing the games and we'll pick a team based on that.
“Early on it was very restricted in terms of what we could do but we've had a really good week's training this week.
“It's not just the players who've been playing the games, it's been important for the players who haven't played a lot of games to get some football into their legs and that's what we've tried to do this week.
“I've had a great response from the players in terms of their attitudes, the other coaching staff who are helping us – Lee Bullen, Steve Haslam and Andy Holdsworth have been terrific and everyone's been together.”
Marriott suffered a year-ending hamstring injury under then-manager Garry Monk, and it had been expected his loan from Derby County might be cancelled but he is back to compete with January signing Andre Green and others for a place in the forward line.
“He's come back in really good condition, he's got over his hamstring (injury),” said Thompson. “He's looking really sharp, champing at the bit, as is Andre, Patto (Callum Paterson), Josh Windass, Jordan (Rhodes) and (Elias) Kachunga, so there's a few options there which is good. It's something we've not had recently.
“It's good to have options because we're going to need them in the run-in.”
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