Why would AA waste a long haul B788 on one of their shortest (and least important) transatlantic routes? AA have based their B788 fleet at ORD, LAX and DFW, flying routes such as ORD-PVG and LAX-AKL that need to be operated by the B788 and not the B763. The only European routes served by the B788 are their flagship ORD-LHR and the occasional ORD-BCN.
I would say that MAN is at the bottom of AA's list of airports that require an upgrade to the B788.
Also, there's no chance that BA would operate the route. Basing an aircraft at MAN would be wholly inefficient, and AA are in a much better position to operate flights to MAN from their side of the Atlantic.