The 23-year old former Adelaide United striker is on the outer at Greek club AEK Athens following the arrival of former Barcelona and Chelsea star Eidur Gudjohnsen with some reports suggesting he may be on his way back to Australia.
But Burns' representative, Bernie Mandic, said that the seven-times capped Socceroo will remain in Europe as some other clubs are showing interest.
"There have been talks with Sydney but the option Nathan wants to pursue is staying in Europe," Mandic told The World Game.
"There are three clubs in the picture and possibly something may be done before the transfer window closes at the end of August. If not, no problem. We are pretty relaxed about it.
"Nathan has been happy in Greece ... but problem is he wants to be playing more games at this stage of his career, so we will see what happens," added Mandic.