Citing information from Sky Italia, it is claimed officials from the two clubs held a meeting over dinner in Italy, and an agreement was reached.
Spanish newspaper Sport reported a day earlier that Tottenham had lodged a bid of £20 million for the French international, amid interest from Barcelona, despite the Spanish side's own transfer ban.
What next and how much will it cost Milan?
The Tuttomercatoweb report makes clear that Milan do not yet have personal terms agreed with the Monaco star.
With no Champions League football on offer, it is no foregone conclusion Kondogbia would choose Milan despite their glittered history. This at the same time would also be of little help to Spurs.
Milan will have had to pay more than the reported amount from Tottenham. French website Le10Sport claim there are as many as 10 clubs battling to sign the former Sevilla star, and Monaco want a minimum of £25 million for the defensive midfielder.
Spurs may have been beaten to the punch of this deal, or with Kondogbia yet to talk terms with Milan, it could be argued there is still time for them to match or better Milan's offer to the Ligue 1 side.