The Daily Star says United boss Sir Alex Ferguson and his assistant Mike Phelan made a personal check on Oxlade-Chamberlain on Tuesday night and are considering a bid.
Fergie watched the player in action for the Saints at Oldham and the youngster, who is the son of former England and Portsmouth star Mark Chamberlain, scored in a 6-0 victory.
Ferguson was looking at United's FA Cup fourth round opponents. But the main incentive for his trip to Boundary Park was to see Oxlade-Chamberlain.
It is understood United are willing to sign the player and loan him back for the rest of the season.