United boss Louis van Gaal has been extremely active in the transfer market this summer, completing deals to bring Memphis Depay, Matteo Darmian, Sergio Romero, Bastian Schweinsteiger and Morgan Schneiderlin to Old Trafford.
The Premier League giants are understood to remain keen to strengthen even further before the closure of the summer window, and Tuttosport [via Metro] reports the club have turned its attentions to Gotze and Draxler.
Van Gaal is understood to be keen to sign at least one of the pair, but the report suggests the Dutchman will attempt to sign both if possible.
Gotze has been linked with a move away from Bayern Munich following a reported fallout with manager Pep Guardiola and also has interest from Serie A giants Juventus.
Draxler is a long-term target of Arsenal, however, the Gunners have been unable to prize the Schalke star away from the Veltins-Arena.
According to Metro, United would have to stump up at least £86.6m to sign both players
Arsenal READY to make move for £55m Karim Benzema ALTERNATIVE
Tottenham keen to SWOOP on Man United star & Arsenal target
Man United to COMPLETE £17.7m midfielder signing, personal terms AGREED