Kessie will be out of contract at the end of the season and he has so far rejected offers of a new deal from AC Milan.
The midfielder is likely to leave the Rossoneri on a free transfer in the summer as his wage demands are too rich for the Italians, and his situation has put several top clubs on alert.
Juventus and Inter are interested in snaring him away from AC Milan, while Barcelona have continued to be in contact with his entourage over taking him to the Nou Camp.
But according to Catalan daily Sport, Kessie has already received a lucrative contract on his table from Tottenham and is a priority for the north London side.
Paratici is desperate to win the race for Kessie and put him at the disposal of boss Antonio Conte.
The north London club have offered him a big salary to move to the Premier League at the end of the season.
Barcelona remain at the window but they are not prepared to go overboard for him in the summer.
Kessie remains on the shortlist of several clubs, but he is likely to go to the highest bidder in the coming months.
