French club Lyon have made an approach to sign Koscielny, 33, who only has another year left to run on his contract in north London.
Rennes, Bayer Leverkusen and AC Milan have all been keeping an eye on developments regarding Koscielny, who the Gunners are weighing up selling to raise funds for Unai Emery.
The Europa League finalists are refusing to let Koscielny, who has served them for nine years, leave for nothing and instead want £10million.
But in a dramatic turn of events they could now offer him an extra year on top of his existing deal to match the terms being offered from France.
It could mean Lyon will now revive their interest in landing Manchester United’s Eric Bailly.
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Bailly has fallen out of favour at Old Trafford but could be key if United do not buy a new defender.
Lyon might even target Sampdoria’s Joachim Andersen, who is ironically a target for Emery.
Andersen has forged a reputation as one of Serie A’s most promising defensive prospects.
Earlier this week, the Dane opened the door to potentially bringing down the curtain on his spell with Sampdoria.
“It could be time for me to further my career,” Andersen said. “I have loved my time in Sampdoria.
“The fans, the president, the staff, the players, the city – but maybe it’s time to move on to develop further.
“There are a number of interested clubs from Europe’s biggest leagues who are discussing with my agent and I’ll be making a decision shortly together with my family and my agent.
“It’s very important to me that Sampdoria can also benefit from an eventual transfer. It’s not all about me. I have so much to thank this great club for.
“Without Sampdoria, I wouldn’t have had the opportunities I have had to this point.
“I have dreams of playing in the biggest clubs in the world and the biggest leagues in the world – I’m lucky enough to already be playing in one of them.
“I think I have a pretty broad football education and I don’t see why I shouldn’t be able to adopt to most leagues. But I’m not saying it would be easy.”
Even if Koscielny stays put, Arsenal are likely to make moves in the transfer market to snare a new centre-back.