The Brazil international has featured just fine times in the Premier League this season, with Mauricio Pochettino preferring him in the UEFA Europa League - where he has made seven outings.
Paulinho also struggled to hold down a regular spot under Pochettino's predecessor Tim Sherwood.
And Cruzeiro's director of football Alexandre Mattos has revealed the Brazilian Serie A club are interested in the 26-year-old.
"If Paulinho has the possibility to leave, all players first think of Cruzeiro," Mattos told Radio Itatiaia.
"Regardless of the bond with another club, such as Corinthians, I'm sure he would be interested in Cruzeiro.
"The scenario could work with a loan, agents have already put this to several clubs in Brazil in fact.
"Tottenham have not yet officially offered the player, but we will await their stance."
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