Harry Redknapp is a big admirer of the combative midfielder who played for him at Portsmouth and his arrival would help bolster a midfield depleted by injury.
Muntari has failed to secure a regular first-team place in Jose Mourinho's team and wants a return to the Premier League.
The only complication is his involvement with Ghana at the Cup of African Nations in January but Tottenham are understood to be prepared to wait until the end of the tournament to finalise a deal.
Spurs are also looking at Brazilian central midfielder Sandro, who plays for Internacional in his homeland while Redknapp is also expected to bring Adel Taraabt back into the first-team squad.
Taraabt will return from a successful loan spell with Queens Park Rangers in January to provide cover for Aaron Lennon.
It is believed Portsmouth goalkeeper David James also remains a January target.