The Ukrainian speedster spent last season on loan at Mechelen and clocked 24 appearances across all competitions for the club, scoring five times.
He did enough to cause Mechelen to want him back and the Celtic man also wants to play his football at the Achter de Kazerne once again.
Shved was spotted in the centre of Mechelen at the weekend and was even filmed on Tuesday running laps in the stadium in a club training shirt.
However, according to Belgian daily Gazet van Antwerpen, no deal has yet been done between Mechelen and Celtic.
The Ukrainian is firmly out of favour at Celtic, but Mechelen are still in talks with the Scottish giants in a bid to find an agreement.
Shved, 24, has another two years left on his contract at Celtic Park.
He has made just three senior team appearances for Celtic, scoring a lone goal and looks unlikely to add to the total.
