Schneiderlin, 25, joined the Saints from Strasbourg back in 2008, and has now played almost 300 games for the club having been a mainstay of the side during their rise from League One to the Premier League.
The Frenchman now has nine caps for his country and has cemented himself as one of the finest midfielders in the Premier League after another superb campaign on the South Coast.
Yet, just as Calum Chambers, Luke Shaw and Adam Lallana left St. Mary's Stadium last summer, Schneiderlin looks set to do the same this time around - and it's now believed that United are hoping to pip rivals Arsenal to his signature.
The Mirror are reporting that Red Devils boss Louis van Gaal is lining up a move to sign Schneiderlin from under Arsenal's nose as he looks to improve his midfield options at Old Trafford.
Ander Herrera enjoyed a promising first season in Manchester but Schneiderlin would certainly improve United's midfield, and the suggestions are that a deal for Schneiderlin could be moving closer ahead of the summer transfer window.
United are moving quickly this summer having already snapped up PSV Eindhoven winger Memphis Depay, and Schneiderlin would be another impressive move from United, who can now offer Champions League football to targets once again - which could be a deciding factor in their pursuit of Schneiderlin.