The Daily Mail says Levy has flown in from his Miami home to press ahead with negotiations for Lamela and step up interest in his team-mate Pjanic.
The quest for Argentina forward Lamela, 21, shows the preference of manager Andre Villas-Boas for the best South American talent. Spurs hope to sign him before Sunday's home Premier League clash with Swansea.
Bosnian Pjanic, who has spent two years at Roma after moving from Lyon for £8m, is also on Tottenham's wanted list.
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