Gervinho has signed a one-year contract extension with Roma, the Serie A club have announced.
Jack Cork wants to open new contract talks with Southampton, but remains focused on establishing his first-team place.
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."