The 22-year-old forward signed for Spurs in a £25.7 million move from Roma last summer, but made just 17 appearances in all competitions as he struggled to adapt to the Premier League.
|14/1||Tottenham are 14/1 with Bet365 to win the FA Cup in 2014-15|
"Lamela is a dream that we haven’t been given a chance to realise, simply because Tottenham don’t want to put him on the market," Ausilio told Gazzetta dello Sport.
Inter are attempting to reshape their squad after a disappointing campaign in which they finished in fifth position, 42 points behind Serie A champions Juventus.
The Nerazzurri have already added Nemanja Vidic to the side on a free transfer from Manchester United, and while Lamela is on coach Walter Mazzarri's radar, Thohir conceded the power lies with the selling clubs.
"Mazzarri likes Lamela and Luiz Gustavo but everything depends on the transfer market," he said.
"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."
Lamela scored 19 goals in 62 appearances for Roma before his big-money move to White Hart Lane, but following the sacking of Andre Villas-Boas in December, he failed to convince Tim Sherwood of his talents - though new coach Mauricio Pochettino will now have the final say over the forward's future.