Welbeck was widely expected to join Tottenham before Monday's deadline, but with around five hours to go reports emerged suggesting he had undergone an Arsenal medical.
Arsenal quickly denied that and say there is no agreement yet, but both clubs are working on completing a permanent deal before 11pm.
The proposed transfer comes despite Arsene Wenger's repeated insistence that he has enough cover in his current squad for injured striker Olivier Giroud, who is out until the New Year.
Welbeck went to the World Cup with England this summer but is surplus to requirements at Old Trafford under Louis van Gaal.
His sole start this season came in the League Cup defeat at MK Dons, and United have since struck a deal to sign Radamel Falcao on loan from Monaco.