Vidal, who knows Sanchez well from their time in in the global set-up, has already talked up the merits of Bayern.
Arsenal are thought to want £50m for the 28-year-old but Wenger has insisted he would rather keep him for 12 months and lose him for nothing next summer.
Vidal told BILD (via goal): "We'll see if Alexis is coming".
'I know him very well. "And we would certainly improve with him", Vidal said.
And Vidal thinks Sanchez, who has been linked with Bayern and PSG, would be the flawless fit for the Bundesliga champions and has urged him to join him in Munich.
But Hitzfeld, who led Bayern to five Bundesliga titles and a Champions League crown, said the club needed to move quickly to secure a good deal for the Chile worldwide.
Sanchez recently played it coy while asked by a German reporter if he would join Carlo Ancelotti's side.
28-year-old Sanchez is thought to be keen on a reunion with Pep Guardiola, but City bosses have a hard task ahead in convincing Arsenal to sell to a Premier League rival.