When Fuchs joined City from Schalke in 2015, he signed a three-year contract, the left-back open with his plans to head to America after a stint in the Premier League.
But after the title win, he added another year to his deal.
A further contract extension seems unlikely, but Rodgers remains coy.
The City manager did, however, praise the impact of the 32-year-old Fuchs, who came off the bench in the 2-1 win at Burnley last time out, strengthening the away defence as the Clarets pumped balls into the box.
It was just Fuchs’ eighth appearance in all competitions this season, the Austrian finding himself back-up to Ben Chilwell this term. But with the England star linked to Manchester City, there is a danger Leicester could lose both left-backs.
“We’ve had a couple of conversations, but after the international break, we’ll probably look deeper into it,” Rodgers said on Fuchs.