The winger was on loan at Galatasaray last season and made a positive impression on the Turkish giants during his stint.
They want him back, this time permanently, and have been holding talks with Norwich to try to agree a deal this summer.
No agreement has been reached yet and, according to Turkish daily Sabah, Galatasaray are attempting to strike a compromise with Norwich, who want €12m.
Galatasaray believe there may be a middle ground where a sum acceptable to both clubs can be agreed.
Rashica is claimed to want to make the switch to Istanbul, completing a permanent move this summer.
The winger was not included in Norwich’s matchday squad for their Championship opener against Hull City on Saturday.
He made 26 appearances in the Turkish Super Lig for Galatasaray last season, finding the back of the net four times and providing seven assists.
