The former City right-back is a free agent after his contract was allowed to expire at the Etihad Stadium earlier this summer, with moves to both Crystal Palace and Stoke City failing to materialise.
The 34-year-old would prefer to continue playing in the English top flight but his previous £90,000 per week City wages are believed to have scared away a number of interested suitors.
Italian side Torino expressed a recent interest but it is the Foxes who are suggesting a potential compromise for the ex-France international, who may even be willing to accept a pay-as-you-play deal, coupled with a decent basic salary of around £50,000 per week.
It is understood Leicester boss Craig Shakespeare may be open to signing the full-back on a short-term deal for the rest of the campaign, with the promise of something more concrete if he can help the former Premier League champions solidify their leaky backline.
The one-time Arsenal man has kept himself in decent shape and is ready to answer the Foxes’ call if the two camps can now make the numbers work.
Arsenal are lining up a move to bring Sevilla midfielder Steven Nzonzi back to the Premier League this summer.
Tottenham are reported to have been offered Lyon playmaker Nabil Fekir following the collapse of his move to Liverpool.
Manchester United are ready to launch a straight £60million bid to try and sign Chelsea star Willian, reports have claimed.
Liverpool are being linked with a swoop for Inter Milan striker Andrea Pinamonti, but have been warned he wants regular action.
Borussia Dortmund are reported to have dropped all interest in Chelsea striker Michy Batshuayi and are looking elsewhere.
Sevilla are bracing themselves for interest in Steven Nzonzi and have lined up a replacement in the form of Marcos Llorente.