The Portuguese side see him as a potential new number 10, although a deal is far from completion.
Boss Julen Lopetegui has refused to rule out making further signings to bolster his squad for this season, and is thought to be targeting both a centre-back and potentially a number 10.
However, he has so far been unable to secure deals for either Oliver Torres or Lucas Lima, with both of those players looking anything but secured.
That has led him to turn his interest to Argentine Lamela, claims A Bola, with the player currently out of favour at Tottenham after failing to impress since his big-money move to White Hart Lane in 2013 in the wake of Gareth Bale's sale to Real Madrid.
His standing in the Spurs squad was demonstrated in the recent loss to Manchester United, with Mauricio Pochettino having elected to start Mousa Dembele on the right wing ahead of Lamela.
Tottenham unlikely to recoup Lamela fee in sale
Lamela may fancy the move given the position he currently occupies in the Spurs squad, with it looking unlikely that he will be a regular starter this season in England - a standing he could enjoy in Portugal.
Having said that, he may be determined to stay in England and prove himself worthy of the sizeable fee Tottenham paid for him two seasons ago, with him having showed flashes of his quality but never produced on a consistent basis.
Whether Spurs would be willing to sell is also an interesting question, given they are unlikely to recoup anything near what they paid for him in any sale.
Mauricio Pochettino may feel keeping him in the squad would be a better option, with there every possibility that he will come good in the future.