Rose is surplus to requirements at Tottenham and has not been given a squad number for the new campaign as the club look to move him off the books.
He has had interest from several sides, including Italian outfit Genoa, but now interest from the Serie A side is now cooling.
Rose now looks unlikely to be making the move to Genoa.
He has admirers in Spain and Turkey, along with from one club in England, but there is a risk he could continue at Tottenham.
If no solution can be found for Rose before 5th October, he will stay put at Tottenham and not have a chance to leave until the next transfer window opens in January.
The left-back spent the second half of last season on a loan stint at Newcastle United.
He still has a further year left on his contract in north London and could see it out to then leave as a free agent.
Tottenham recently signed a new left-back in the shape of Sergio Reguilon.