Evans is currently away on international duty with Northern Ireland after suffering a disappointing Premier League season with West Brom, that ended with the 'Baggies' being relegated from the English top flight.
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 contract in the Midlands.
Northern Ireland will take on Costa Rica on Sunday and spekaing ahead of that game, O'Neill expressed his belief that Evans could play for a top-six side.
"He's certainly capable of that," O'Neill insisted.
"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."