The 23-year-old has stated that he will remain with the French club for the rest of the season, despite the Gunners reportedly planning to table a bid for the playmaker in the new year.
"I will not leave this winter. I have started this season for Sochaux and I will finish the season in Sochaux," talkSPORT quotes Martin as saying.
"That is clear and I have discussed it with the management here. I'm not one to leave halfway through a season."
Martin did not rule out a move to the Emirates next summer.