The Southampton starlet, 17, is believed to be the player who United boss Sir Alex Ferguson was referring to on Saturday when he revealed that he tried to make another signing in the January transfer window.
Oxlade-Chamberlain was reported to be close to joining the Gunners during the January transfer window, prompting Ferguson to step up his interest.
Arsenal were on the verge of agreeing a £10m package - £5m cash plus add ons - before the United manager went to see Southampton demolish Oldham 6-0, with Oxlade-Chamberlain scoring the first goal, and made his mind up to launch a swoop.
United chief executive David Gill held face-to-face talks with Southampton chairman Nicola Cortese at the FA Cup fifth round clash and, although the Saints decided not to sell, Ferguson achieved his goal of stopping the youngster from joining Arsene Wenger's squad.
United have apparently indicated that they are willing to wait until the summer and would top any Arsenal fee and wages on offer to the teenage winger, who is being tipped to eventually develop into a central midfielder.