The 31-year-old's representative, Dino Lamberti, has spoken to the Premier League champions following Inler's disappointing first season in England, Press Association Sport understands.
No decision has been made, but Inler hinted last season he would be prepared to leave the King Power Stadium following his lack of action.
He admitted in January he had other options, but stayed to be loyal to boss Claudio Ranieri, yet Schalke have a long-standing interest after they lost out to Leicester for his signature last summer
Inler failed to play for the Foxes after January and was dropped for Switzerland's Euro 2016 campaign, despite captaining them during qualifying.
Head coach Vladimir Petkovic warned his then-skipper, who has won 90 caps, in March he faced missing out on the tournament in France and he was eventually left at home after playing just 194 minutes in the top flight
The former Udinese man made just five league appearances for the Foxes last season as they won a shock Premier League title by 10 points.
He still earned a medal, but Inler's last league appearance for Ranieri came in their 0-0 draw with Manchester City in December, with his final game coming in January's FA Cup exit to Tottenham.
He joined from Napoli for £5million last year, but fell behind Danny Drinkwater and N'Golo Kante in Ranieri's plans, although the Foxes are facing a battle to hold on to France international Kante this summer.
The Foxes have been linked with a move for Nice midfielder Nampalys Mendy who would add further competition for Inler
Source : PA
Source: PA