Messi rates Rooney among the best players in the world and feels he would be an instant hit at the Nou Camp.
He is pessimistic regarding Barca's chances of luring the England striker away from Old Trafford, but knows you can never rule anything out.
The Argentina superstar believes Rooney would be successful at any club on the planet, with his passion for the game setting him apart from most of his contemporaries.
"It would be a dream to play with Rooney if Manchester United ever came to the point where they needed to sell him," Messi said in the Daily Star Sunday.
"I would personally go to the Barcelona president and ask that he be signed myself.
"There are always a handful of players in the world at any one time who can go down in the footballing history books.
"At the moment, there are maybe (Cristiano) Ronaldo, Rooney, Xavi and one or two more - but I can't think of one that plays with the desire of Rooney.
"We all know football players at the top level are blessed with high wages, it's no secret. But Rooney would play for 100 euros-a-week. You can see the fire in his eyes.
"It's that fire which makes him the best of the best."
Messi feels that were United to ever cash in on Rooney, he could easily become the most expensive player in history.
"If Rooney is ever sold, I think he will become the first 100million euro player," he added.
"With all respect to Ronaldo (who left United for Real Madrid in an £80m deal last summer), I think Rooney is a more important player for United than he was.
"Ronaldo's ability is undoubted but Rooney is not only the talent but the heart of the Manchester United team.
"I don't know if I will ever play with him but, if he ever wants to leave, he is one of the few talents that can improve this Barcelona team."