Bayern increased their bid from £30 million, which was reportedly rejected by the west London side. The latest offer is believed to be the fourth from the Bavarian giants.
Chelsea assistant Gianfranco Zola recently confirmed Bayern's interest in the 18-year-old, while adding that the Premier League club had also proposed a new contract to the player.
However, Aarons reports that Hudson-Odoi - who has 18 months remaining on his current deal - has refused to enter discussions with Chelsea's hierarchy.
The tug of war is putting Chelsea manager Maurizio Sarri in a tough position, but he assured reporters Monday that Hudson-Odoi is very much in his first-team plans.
"I think so. He's ready," Sarri said. "Of course, we have very important players in the same position, so do you want Willian or Pedro on the bench? I can play with only two wingers, three is difficult.
"But I think now (Hudson-Odoi) is ready. He can play, but of course sometimes he will be on the bench, like Willian or Pedro, but now I can start to consider him at the same level."