The 19-year-old has been training with Spurs' development squad for the past fortnight, but it's understood he's yet to agree terms with the north London club.
If the transfer goes ahead it's understood a sell-on fee of between 10 and 20 per cent will be included for the Isthmian League Premier Division club.
However, the deal might have been complicated after Tanner picked up an injury in Tuesday's 2-0 win over Cray Wanderers.
Brighton have also been linked with an interest in the wideman, but it's believed Lewes rejected a permanent offer from the Seagulls where he'd rejoin the club on loan for the remainder of the season.
Spurs have so far had a very frustrating window with a number of targets being snapped up by other teams.
Adama Traore was wanted by Antonio Conte but the club didn't lodge a bid and he has subsequently joined Barcelona instead.
Liverpool, meanwhile are flying a team to South America as they try to push through a late move for Porto forward Luis Diaz, who had been a prime attacking target for Spurs beforehand.
It's believed Spurs are now planning a move for Juventus attacker for Dejan Kulusevski.
Kulusevski, 21, has made 20 Serie A appearances for Juventus this season but has only started in half of those and scored just one goal.