Amiri plays for German side Hoffenheim and is expected to leave the club 'no later than the summer'.
Tottenham are reported to be long term admirers of the playmaker and their interest in reported to be the strongest, despite Manchester United and Arsenal being keen.
A move this January is unlikely after he suffered a foot injury at the weekend which will sideline for 'a few weeks'.
Amiri, 21, is a German under-21 international and has committed to play for the senior team despite advances from Afghanistan to convince him to play for them.
Amiri has scored four goals this season for seventh placed Hoffenheim and provided two assists.
He could be an alternative to Ross Barkley for Tottenham, who Spurs passed on this month, allowing him to quit Everton for Chelsea unchallenged.
There is no word on whether Tottenham plan to bid this month, but Amiri is said to be keen to leave Hoffenheim this summer for a new challenge, and the North London side's long standing previous interest puts them in a strong position.
Amiri is determined to play in the Champions League, although first Tottenham need to ensure they qualify for next year's competition if they are to get their man.