The former Southampton star also believes the midfielder is more than capable of starring for a top four side, regardless of where he ends up.
Both clubs have been linked with a move for the French star over recent months (the Express mentions both clubs as interested) after another impressive season with the Saints has increased interest in his services.
Arsenal in particular have been in need of a defensive midfielder for some time and it remains a weak point despite the emergence of youngster Francis Coquelin last season.
United are likely to be looking for a long-term replacement for Michael Carrick at some point in the future and Le Tissier believes they are in more need of the midfielder than the Gunners.
"Out of the top four clubs, I think Manchester United are more in need of him than Arsenal,” he said.
“Arsenal have got a lot of midfield players. Would he be that much better than what they have already got? In terms of needing somebody in that position and being light in that position, I think Manchester United are more in need of him than Arsenal are."
Schneiderlin was widely expected to leave the club last summer as they lost the likes of Luke Shaw, Calum Chambers, Adam Lallana and Ricky Lambert in a number of big money moves.
They managed to hold onto their man though and he went on to play a key role in their success under new boss Ronald Koeman, and Le Tissier says he is more than capable of turning out for a top four side.
“He can play for a top four team comfortably,” he added.
“He is very accomplished in that [defensive midfield] position. As our team has improved, he hasn’t looked out of place in any of the places he has performed.”