Ajeti is surplus to requirements at Celtic and has been tipped to move on from the Scottish side in the ongoing summer transfer window.
However, he is in no rush to move to a destination where he would have to take a substantial pay cut, with talk he earns around €1.2m net per year.
He could well have an option to return to former club Basel as they are toying with the idea of a swoop, according to Swiss daily Blick.
Basel are keen to have players in the squad that identify with the club’s DNA and Ajeti, a former Basel star who was born in the city and came through the club’s youth ranks, fits the bill.
The St Jakob Park outfit would be unlikely to be able to match the wages that Ajeti currently takes home at Celtic however.
He has a year left to run on his deal at Celtic Park and could have more lucrative proposals than Basel.
Ajeti, 26, made 23 appearances on loan at Austrian side Sturm Graz last season and scored four goals.
