Clyne, 29, left Liverpool when his five-year deal expired in the summer and is still without a club.
The 14-time England international has suffered badly with injuries in recent years, limiting him to just ten appearances for Liverpool in the past three seasons.
He spent the second half of the 2019-20 season on loan at Bournemouth, managing 15 appearances.
Sabaly is wanted by Spartak Moscow and with the Russian transfer window open until October 17, he could still move.
Spartak and Bordeaux have yet to hold formal talks for Sabaly, but the Muscovites have sent out feelers.
And should he leave, Clyne would then become a serious option for Girondins.
Bordeaux are also seeking a way out for Serbian defender Vukasin Jovanovic, with Russia also an option for him.