The Gunners have enjoyed a strong campaign, trailing Premier League leaders Liverpool by 13 points with five games left. Liverpool need one win to secure their 20th top-flight title.
However, Arsenal have excelled in Europe, reaching the Champions League semi-finals after a 5-1 aggregate rout of Real Madrid, setting up a clash with Paris Saint-Germain.
Partey, 31, has been central to Arsenal's European success, but with his contract expiring, Barcelona and Atletico Madrid are circling.
Hargreaves, speaking on Rio Ferdinand's YouTube channel, backed Wharton as the ideal successor. "Adam Wharton's vision is exceptional," Hargreaves said. "If Partey leaves, he's the one. His touch and game-reading are top-class. Arteta would love him."
Ferdinand compared Wharton to ex-United star Michael Carrick. "He can move the ball forward with great passing," Ferdinand said. "He'd be a brilliant United signing, like Carrick."
Wharton, 20, has shone at Palace and earned an England Euro 2024 call-up, with Real Madrid also reportedly interested. Arteta, quizzed last week on Partey's future, said, "There's progress with all players. (Sporting director) Andrea Berta and the club will handle it."
He added, "The intention is clear, but it's for them to decide."
With a Champions League semi-final looming and transfer decisions pending, Arsenal face a defining moment.