Leeds and Burnley have four games remaining to secure survival while the Toffees have five fixtures to try and climb out of the bottom three.
Wilson, who is part of a Newcastle squad that have climbed towards safety in the last couple of months, believes that Leeds' run of fixtures will make things difficult for them.
“If I had to choose from the remaining fixtures, it looks like Leeds could be in trouble," he told the Footballer's Football Podcast.
"We were in that position not so long ago and we managed to get ourselves out of there thankfully. I just feel with the remaining fixtures and the little bit of momentum that Everton have now got by beating Chelsea, that could be what they need to lift themselves out.
"Burnley have done tremendous to get themselves into that position that they are because they were down and out but they are the ones who are in form at the moment. I think it's Leeds who are in trouble.”
Leeds have Arsenal, Chelsea, Brighton and Brentford left to play while Burnley face Aston Villa twice, Tottenham Hotspur and Newcastle. Everton's remaining games come against Leicester City, Watford, Brentford, Crystal Palace and Arsenal.
Wilson was relegated with Bournemouth before joining Newcastle and said of that experience: "I have [been relegated with Bournemouth] and it’s not nice, it’s not nice at all. It obviously impacts the whole club, it impacts yourself and everyone associated with it.
"It’s not something you want to experience as a player and you don’t want anyone else to experience it either. I just feel when you're in that position in the league, it’s difficult sometimes, you don’t want to drop down into the Championship.”