Lamela was considered a top target for Inter in the transfer window following a difficult debut season in England for the Argentine due to poor form and injuries.
Sporting director Piero Ausilio has confirmed that there was interest from the Italian giants, but that Spurs were unwilling to begin negotiations over the sale of the 22-year-old.
"Lamela is a dream that we haven't been given a chance to realise," Ausilio told Gazzetta dello Sport. "Simply because Tottenham don't want to put him in the market."
Spurs signed Lamela from Roma last summer for a club-record fee in the region of £30m.