The London club are expected to lose Gareth Bale to Real Madrid for a world-record fee in the coming days, but are believed to have identified the Argentine attacker as the ideal replacement.
And, when asked about reports that Lamela had arrived in London on Wednesday ahead of a medical, Villas-Boas explained that he expects "further news in the next few days".
In his press conference ahead of Thursday's UEFA Europa League clash with Dinamo Tbilisi, Villas-Boas admitted for the first time that Bale is close to sealing a big-money switch to La Liga.
The Welshman netted 26 goals in 44 appearances for Spurs last season as they narrowly missed out on qualification for the UEFA Champions League.
The White Hart Lane outfit will now hope that Lamela, who scored on 15 occasions in 33 Serie A outings last term, can fill the void left by Bale's departure to Madrid.
Lamela, a graduate from River Plate's youth academy, has three senior caps with Argentina to his name.
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