Kessie was heavily linked with leaving AC Milan this summer, but he has remained at the club beyond Tuesday’s transfer deadline.
The midfielder has entered the final year of his contract at the San Siro and is yet to commit to a new deal; he has been linked with interest from several clubs across Europe.
Chelsea and Spurs were among the clubs credited with interest in Kessie during the recently concluded summer transfer window, but the Premier League duo did not make any concrete moves for him.
However, according to Italian broadcaster Sportmediaset, both London outfits remain admirers and are plotting a free transfer swoop next summer.
If Kessie does not sign a new deal at AC Milan he would be able to sign a pre-contractual agreement as soon as in January with a potential suitor.
The Rossoneri had to witness two of their former key players in Gianluigi Donnarumma and Hakan Calhanoglu walk away for free this summer and they are determined to avoid a similar scenario with Kessie next summer.
It remains to be seen whether the Ivorian will sign a new contract at AC Milan, and whether Chelsea and Spurs will get an opportunity to sign him as a free agent.