Ligue 1 outfit Sochaux have admitted to holding an interest in Maurice Edu, with the Rangers midfielder sat top of their winter wish list.
It is understood that the French side have already had one approach for the United States international knocked back.
They are refusing to give up the chase, though, and an improved bid is believed to be in the pipeline.
Edu has been a prominent figure in the Rangers side this season, making 24 appearances and scoring two goals.
It remains to be seen whether Ally McCoist would be prepared to part with the 25-year-old, but Sochaux are willing to keep pushing the issue.
"We are interested in bringing Maurice Edu to Sochaux," the club's assistant coach Stephane Gilli told STV.
"We have two or three other midfield targets but it's fair to say that Edu is our number one target for the midfield position.
"I cannot say if we have made an offer to Rangers. We will be discussing transfer strategies with the president of Sochaux this evening (Thursday)."