According to The Sun's Daniel Cutts, Bayern are interested in Martial but do not want to spend more than £50 million on him, leaving them £20 million short of United's valuation.
Red Devils manager Jose Mourinho is a longtime admirer of Lewandowski, and so United will propose an exchange in which the striker is used as a makeweight in any deal sending Martial to Germany.
An unnamed source told Cutts:
"Bayern are still keen, and United have been after Lewandowski for a long time and want him. His agent is close to Jose and United, and he is keeping them both in the loop along with Real Madrid.
"This is all down to whether he wants to go, and Bayern are happy for him to leave. It's up in the air. Bayern want Martial to take over from Ribery but don't want to pay the excessive fee being asked for."
In May, Lewandowski's agent Pini Zahavi announced the Pole, who has three years remaining on his contract, wanted to leave Bayern.
Munich boss Niko Kovac has moved to shut down talk of an exit, though, per Sky Germany (h/t Goal's Ronan Murphy):
It's hardly surprising Bayern are desperate to keep him, given he has been a consistently prolific hitman for them:
United's interest is similarly understandable, as the chance to sign someone of his quality does not come around too often.
However, Lewandowski occupies the same position as Romelu Lukaku, and it's difficult to imagine the pair fitting in the same system.
After splashing out an initial £75 million on the Belgian last year, United may want to think twice about bringing in someone who would knock him down the pecking order, particularly as his presence in their squad ensures they're already covered at centre-forward.
While Lewandowski could be an upgrade, the Red Devils have other more pressing needs they should address if they're determined to receive a player in return for Martial.