The London club are said to be weighing up a move for the Brazilian forward after technical director Franco Baldini identified him as a top target, according to Football Direct News.
The San Siro side have endured a desperately disappointing campaign that means they will most likely miss out on European football next term.
Milan currently sit 10th in the Serie A table, whilst their Champions League campaign came to an end last week following defeat to Atlético Madrid.
A source close to White Hart Lane has said that Baldini is looking to utilise his contacts in Italy to bring in Robinho as a replacement for Jermain Defoe, who left last month to join MLS side Toronto FC.
Former Manchester City man Robinho will have two years remaining on his contract at the San Siro when the transfer window reopens.
It is thought that the 30-year-old may welcome a return to the Premier League and a move Spurs would see him join compatriots Sandro and Paulinho.
