The winger has been linked with Inter and Juventus and is desperate for first-team football to boost his World Cup ambitions after a disappointing start with Spurs.
The Argentina international has started just three Premier League matches since his 36 million euro arrival from Roma in the summer and has largely been restricted to a substitute role.
Speculation in Italy is rife than Inter is looking to secure a loan deal for Lamela, while he has also been linked with a permanet move to Juventus in a swap for striker Mirko Vucinic.
Spurs, however, are determined to keep Lamela in January unless there is a drastic change in circumstances, especially as manager Tim Sherwood deals with an injury crisis.
Lamela was given few opportunities under former boss Andre Villas-Boas and Sherwood has yet to make a judgement on the attacker, who missed the north London derby defeat to Arsenal with a thigh injury, but is expected to be fit to face Crystal Palace on Saturday.
The veracity of quotes attributed to the 21-year-old's father this week has been questioned but Lamela is undoubtedly frustrated with his lack of form and opportunity at White Hart Lane.
The Argentine's agent is believed to be courting interest in his client, who has scored just one goal this season, in a Europa League match against Sheriff, and has settled slowly in London having arrived unable to speak any English.
A return to Serie A - where he scored 15 league goals last season - would be the most logical step for Lamela in order to stake his claim for a place in Argentina's squad for the World Cup.
Spurs want to give midfielder time to settle and believe that a return to Italy would be counterproductive to their long-term plans for the former River Plate star.