The 26-year-old spent a year out after suffering a hip injury in October 2016 which needed two surgical procedures to correct the problem.
His return to the first team in November was thought to be the precursor to resuming his first-team career. However, Tottenham signed Lucas Moura from Paris St-Germain during the January transfer window casting doubt over Lamela’s future at the north London club.
The Nerazzurri are keen on the 23-times capped Argentinean, taking him back to Serie A after his five-season spell in the Premier League.
Lamela spent two seasons with Roma and scored 21 goals in 67 appearances for the Giallorossi. He departed for White Hart Lane in a £30m deal during the summer transfer window in 2013.
While Lamela is reportedly open to returning to Italy, there is little sign that Tottenham are ready to sell. However, with new stadium costs to fund from this summer, the north London club may be persuaded to inject funds into their transfer budget through sales.
Much will depend on whether the expected bids for Harry Kane, 24, and Dele Alli, 21, arrive. If the much-speculated interest in the pair materialises into bids, Lamela may find himself staying at White Hart Lane for another season at least.