Wright believes the 26-year-old forward has yet to reach his full potential, but must perform at an international tournament to cement his status.
He told Absolute Radio: "Wayne's [Rooney] what, 26-years-old? I think he's still got plenty of time to get to a tournament and show people that he has got what it takes to be one of the greats.
"I think he deserves it with the time he's been in the game and the pressures he's had to deal with in the public eye from a young age up to this point."
|15/4||Wayne Rooney is 15/4 to be the first goalscorer against Stoke on Saturday with Bet365|
"The Xavi's the Iniesta's, the Pirlo's - they've got the big medals as well as the Champions League one.
"Messi, Ronaldo, when they finish, they're going to go down as greats and I think Rooney will as well, but I feel that the real greats, they win the Euro[pean Championship] medals, the World Cup medals.
"I think, on ability, all three of them, Ronaldo, Messi and Rooney, should all be in that bracket of players who have done that and that is how you become truly great."
Rooney's Manchester United side face a tricky home clash with Stoke in the Premier League this weekend, but Wright, 48, feels that Sir Alex Ferguson's men will edge the game.
"Should be a good game, you know. Stoke are showing good form - I think they're showing the second best defensive record in the Premier League - and United have got quality up front," he continued.
"It might be close, but it's one of those where United are banging on the door and then nick one at the end because that's what United do - they win these games.
"And that's why they'll always be in and around it come the end of the season."