The 30-year-old, who is currently on international duty with Norn Iron, was part of the Baggies side relegated from the Premier League at the end of last season.
Both Arsenal and Manchester City have been linked with moves for the former Manchester United man, who is thought to have a £3m release clause in his Albion contract.
Asked by BeSoccer whether Evans is good enough to play for a top-six club, O'Neill replied: "He's certainly capable of that.
"He had a difficult second half of the season, but so did West Brom as a whole.
"Jonny has all the attributes to play in a top-six side, there's no doubt about that. The price you can get him for is an absolute steal, given what people are buying players for nowadays.
"I expect to see Jonny move in the summer and get a fresh start, hopefully at a big club."
Evans failed to make a single start under then-interim manager Darren Moore as West Brom gave themselves hope of survival with a late-season revival.