The right-back has been linked with a switch to Old Trafford as Jose Mourinho looks to boost his options in the summer.
And Keane believes that it would be to everyone's gain given Coleman would pick up vital European experience that could benefit the Ireland national team.
"I’d love to see Seamus at Man United. It would suit him down to the ground," he said at a fundraiser event before United's EFL Cup final win.
"Obviously, he’s at a very good club in Everton. He isn’t getting any younger. From a selfish point of view, from an Irish point of view, you want players like Seamus playing in the Champions League and getting a taste of football at that level.
"Saying that, joining United might not mean Champions League at this moment in time.”
Despite encouraging Coleman to make the move, Keane is not happy with the way his former club is being run and points the finger firmly at Mourinho.
He added: “I’ve very little time for Mourinho. I look at United and the run they’re on now.
“They’re sixth in the league. People are like, ‘I can see progress’ - [but] they’re sixth in the league. They’ve beaten no one in three months.
“I judge United on the big games. Chelsea and one or two others are coming up now. If you want to play for United and be successful they are the games you have to be winning.”