The London club are apparently ready to offer up to £30 million to secure the Argentine international’s signature.
Jose Lamela, the youngster’s father, and agent Pablo Sebbag are expected to meet former Roma director general Franco Baldini who now works for Spurs.
Tottenham are prepared to offer the 21-year-old a four-year deal worth £3.5 million a year, report the Corriere dello Sport.
Lamela, a left-sided forward, joined the Italian outfit in 2011 from River Plate for around £15 million.
He has scored 19 goals in 62 League games for the Giallorossi since his arrival – 15 of those came during the last campaign.
Milan vice-president Adriano Galliani has admitted that the club are still in “constant contact” with CSKA Moscow over Keisuke Honda.
The Japanese international has been heavily linked with a move to San Siro this summer, with stories emerging for months that the midfielder would join Massimiliano Allegri’s men.
However, a transfer has failed to materialise, and the board member has failed to shed any light on a potential deal.
“Honda? We are in constant contact with the Russian club,” Galliani told Gazzetta dello Sport. “At the moment there is no news.
“But even if there was I couldn’t tell you because we are bound by secrecy with CSKA.”
Inter are still on the lookout for a defender before the transfer window shuts, and have highlighted two prospects according to Tuttosport.
The Turin-based newspaper has claimed that the Nerazzurri could make moves for Paris Saint-Germain full-back Gregory van der Wiel, or failing that, Barcelona’s Martin Montoya.
The Netherlands international has long been a target for the San Siro side, who has failed to establish himself at the Ligue 1 champions since his arrival from Ajax.
Montoya, meanwhile, has been heavily linked with Walter Mazzarri’s men but his agent has insisted that the player’s future remains at Camp Nou.