Sunderland boss Gus Poyet has admitted that Connor Wickham will be sold unless he commits to a new contract.
Hannover admit to being in the market for a new midfielder but deny that Chelsea's Marko Marin is a target.
The 22-year-old striker's three-month stint with the Clarets came to an end after Saturday's 4-0 defeat at Blackpool.
"I think he's done well. He's filled in the various positions, which is the job that we wanted him to do," said Burnley boss Eddie Howe.
"He probably could have scored more than the one goal he got, but I think he can be really pleased with his contribution.
"He's been a joy to work with, he's been very good for the squad, and we wish him well going back to Millwall."