La Gazzetta dello Sport says Tottenham's Director of Football Fabio Paratici approached the LaLiga giants earlier this week to discuss the possibility of a transfer.
Spurs were originally willing to bid around £15m for the Dutchman, but the club could now be offered the opportunity to sign him on a free transfer.
Depay's representatives are currently attempting to negotiate a deal with Barca officials which would see his contract terminated.
The forward has been informed by Xavi that he will have no place at the club next season.
Juventus are also interested in signing Depay.