Roma and Inter Milan are also interested in signing the 20-year-old following a difficult first year in Germany.
Mor joined Dortmund just last summer from FC Nordsjaelland but the wondered struggled for regular game time.
The Turkey international is keen on an escape route to the Premier League, and Everton are now among his potential suitors, according to The Sun.
Dortmund are resigned to losing Mor and will only allow a permanent departure.
The Bundesliga club will also make the winger available for a bargain £12million.
Fiorentina have bid £10.7m are pushing hard, but a switch to England is desired.
Liverpool boss Jurgen Klopp is a big admirer and was in pole position at one stage last summer to sign Mor.
But The Sun add Klopp’s interest could be scuppered by rivals Everton this time, who are ready to continue their spending spree.
Arsenal manager Arsene Wenger, though, has also been asked to be kept updated on Mor’s situation.
The Gunners boss is looking to offload some squad players but still hopes to then strengthen his attacking options.
Meanwhile, Inter could look to sign Mor as a replacement for Ivan Perisic if the Manchester United target leaves.
