Former United forward Ole Gunner Solskjaer has taken over on an interim basis while the club looks for a permanent successor, and Stam thinks that Spurs manager Pochettino is the strongest candidate.
“He's good in building a team, plays attractive football, playing out from the back to score goals and win games. I would say that's my choice.
“I think they can [get him]. There's been a discussion at Spurs about not spending money on players, I think he is the type of manager who wants to invest every year and improve - at United he gets to do that.
“They've got the money to do that. For him, that would be the ultimate step.”
Pochettino has previously stated a desire to take Tottenham into their new stadium as manager, which was originally scheduled to take place this season although delays have seen that move pushed back.
Stam thinks that United will be able to tempt him to leave regardless, insisting they are a bigger club and that they have more money to spend on players.
“The only thing is, and that's a pity for Tottenham, there's always a bigger club and that's United,” he added.
“They've always got that little bit more to spend, they're bigger all over the world. For a manager it's 'if I want to work at the top I need to be there to really show myself'.
“It doesn't matter if they're in the new stadium now or in the next season - if the opportunity is there then he wants to go.”
Stam also backed former team-mate Solskjaer’s appointment on a temporary basis and believes he will have success with the club's younger stars.
“He wants to play attacking football, as a personality he can work with young players, give them a certain feeling, which is what they need,” he said.
“Sometimes they need to be released from something that brings out that feeling of freedom. I think Ole is that type of manager.”