Mesut Ozil's representatives are in talks with a number of clubs, including Fenerbahce and DC United, although the player's priority is to see out his Arsenal contract until the summer.
The midfielder is free to talk to clubs this month with his current Arsenal deal expiring at the end of the season.
If Ozil wants to leave in January, his representatives would have to speak to his club, but the Gunners are yet to receive any direct contact from other clubs.
Ozil's agent, Dr Erkut Sogut, has told Sky Sports News: "In the next seven to 10 days it will be a little clearer."
Ozil was not registered by the Gunners' for the first half of the Premier League season and has yet to be included in a matchday squad in any competition, despite being one of the club's highest earners.
Asked last week whether Ozil, who earns around £350,000 per week and has made it clear he wants to see out his contract at Arsenal, could make a surprise return to his squad in January, manager Mikel Arteta said: "We will see what happens in the transfer window and we will assess at the end of that."
Arteta is being "very cautious" with his treatment of Ozil in case Arsenal fail to sign a creative midfielder during the January transfer window, according to Sky Sports News' Dharmesh Sheth.
Arsenal came close to signing Lyon's Houssem Aouar during the summer transfer window, but their failure to complete a deal for the Frenchman left Arteta short of options in a central attacking midfielder position.
Sheth told Sky Sports News' The Transfer Show that he believes Arteta's preference would be to sign a new attacking midfielder, but in the case that fails, the Spaniard is keeping his options open.
"I think Mikel Arteta is being very cautious with regard to Mesut Ozil this time," Sheth said. "If we rewind back to the summer, it was clear that Mesut Ozil wasn't part of the plans.
"It had gone so far down the line with Ozil that he didn't want to do a U-turn then, so they didn't end up with either in the squad.
"I think he's going to leave it until the final half of this transfer window to decide on Mesut Ozil's future.
"If it transpires that they can't offload enough players to free up enough wages to bring in someone from abroad, then l don't think you can rule out Mesut Ozil perhaps finding some sort of role at Arsenal in the final six months of his contract.
"I think the ideal scenario for Arsenal would be for someone to come in for Ozil - he's eating up £350,000 a week in wages.
"But we can't rule out Ozil still playing a part for Arsenal."
The winter transfer window is open until Monday February 1 at 11pm.
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