Both players are said to be currently unhappy at their current clubs.
Martial is also at odds with United manager Jose Mourinho after reporting late for pre-season training as he attended the birth of his second child.
Martial wants out of United in order to play more regularly. As a result of insufficient game-time last season, he played no part in the French national team which won the World Cup in Russia last month.
The Red Devils are willing to sell Martial on the condition that they receive an offer of at least £70 million. Bayern meanwhile are unlikely to meet this.
In what has so far been an underwhelming summer transfer window for United, they are keen to add Lewandowski to their roster.
He is a lethal striker and undoubtedly has the ability to win games for any of the major clubs in World football.
A source said: “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.”