Postecoglou is suggested to be the frontrunner to take over at Tottenham and will hold talks with the north London club soon, after just completing a domestic treble with Celtic.
The Australian manager is a popular figure at Celtic and fans are hoping he does not answer the call from Spurs.
For Wilson, while Spurs might be a big lure for Postecoglou, he warned there are no guarantees he would enjoy success with them.
He feels Postecoglou still has things to achieve at Celtic, not least the chance to make an impact in the Champions League.
“If he does move there’s no guarantees that moving down south will be a success”, Wilson said on Clyde 1’s Superscoreboard after the Scottish Cup final.
“He’s got this Celtic team playing to his tune so far, in two years, what more could he do with this set of players?
“He can certainly improve in the Champions League and I am pretty certain he would want that; that is the top tier of European football.
“But the lure of Spurs might just be too much.”
Tottenham have no European football on the agenda for next season following a disastrous campaign in north London which saw three different managers at the helm.
