The winger joined Spurs from Roma for 31.7 million euros but made just 17 appearances in all competitions during his first season at White Hart Lane.
The Argentine arrived at White Hart Lane from Roma in a 31.7 million euro deal last summer but has so far failed to produce his best form in England, making just 17 appearances in all competitions.
Inter is hoping to significantly strengthen a squad that finished fifth in Serie A last season and has already snapped up Manchester United captain Nemanja Vidic on a free transfer.
Thohir said that coach Walter Mazzarri is a fan of Lamela and Wolfsburg midfielder Luiz Gustavo, but conceded that the Nerazzurri will not have the final say over whether deals for either player are agreed.
"Everything depends on the transfer market," he told Sky Italia. "Some media report about our interest in [Edin] Dzeko and [Alvaro] Morata, but if their clubs don't want to sell these players we won't do anything."
He added: “Within a couple of weeks we hope to announce a new player. Mazzarri believes in the project and we have to sit down to talk about renewal. In the future, I want the coach to work even more with the young players.
“We want to lower the average age because to be competitive you have to play another way: We need to run, press and attack. Football is different to 15 years ago."