According to The Telegraph newspaper, Conte has pointed to Ivory Coast international Kessie as the primary target for the January transfer window.
Milan would be open to a sale, especially as he is in the final few months of a contract which expires on June 30.
Negotiations to extend have been at a total standstill for several months now, Milan refusing to meet the €8m per season demands set by his agent.
Spurs could free up funds for a swoop because multiple sources today including RMC Sport claim Ndombele is eager for a loan move with option to buy for Paris Saint-Germain.
Conte and director of sport Fabio Paratici are bound to look towards Serie A for a replacement in the Tottenham midfield.
Along with Kessie, another alternative is Roma’s France international Veretout, who is no longer first choice at the Stadio Olimpico after Jose Mourinho brought in Sergio Oliveira from FC Porto.
Tottenham are considering a move for AC Milan midfielder Franck Kessié during the current transfer window to avoid a bidding war for him this summer | @mcgrathmike reports #thfc https://t.co/fO2Mwb73sy
— Telegraph Football (@TeleFootball) January 20, 2022