Spurs manager Andre Villas-Boas has highlighted the Senegal international as the ideal man to strengthen his squad, following news that Sandro will be unavailable for the rest of the season through injury.
Their top target was believed to be Porto’s Joao Moutinho, but the Portuguese playmaker is thought to be unavailable for a January move.
Spurs are said to be attracted to Daime due, in part, to the £3.5m release clause in his contract with the East Londoners.
The White Hart Lane club will face much competition for his signature, with local rivals Arsenal also believed to be highly interested.
Gunners boss Arsene Wenger has been tracking Diame for some time, as he looks to add some steel to his team’s midfield to boost their hopes of a top four finish.
This interest has sparked West Ham into pressing ahead with contract negotiations, as they look to remove the clause from the equation.
He arrived at Upton Park over the summer from Wigan on a free transfer, negotiating a similar deal to that of Demba Ba’s at Newcastle.
AVB has the likes of Scott Parker, Jake Livermore and Tom Huddlestone available to partner Moussa Dembele in midfield, but is believed to be unconvinced by the trio.