Corriere dello Sport reports that both clubs are weighing up moves for the 25-year-old Fiorentina forward, who signed a new contract in Florence last summer through to 2029.
A release clause worth 62 million euros is written into that deal. The window for triggering it runs only until July 15, and it remains unclear whether either Tottenham or AC Milan would be prepared to meet that figure in full.
Milan's interest carries personal weight. Manager Massimiliano Allegri has long rated Kean highly, even through the striker's difficult years at Juventus, and the pair have maintained a strong relationship.
Fabrizio Romano and Matteo Moretto have reported that Kean himself is enthusiastic about the prospect of joining the Rossoneri, attracted partly by their participation in next season's Champions League — a competition Fiorentina have no realistic path to from their current league position. Kean's close friendship with Rafael Leão is said to be a further pull toward Milan.
Fiorentina management has stated a desire to keep Kean at the club, but the situation in Florence has shifted considerably since the contract extension was signed. The team has underperformed this season, and a probable summer restructuring makes the striker's departure harder to rule out.
Kean managed eight goals and one assist in 26 Serie A appearances this term, a step back from the 19 league goals and three assists he contributed in last season's campaign that first drew widespread European attention.
Tottenham's interest has also been reported across multiple outlets, though the original sourcing traces back to Italian sources and has yet to be corroborated by senior transfer journalists. Head coach Roberto De Zerbi, recently appointed at the Tottenham Hotspur Stadium, may be shaping a revised attacking setup for next season, and Kean fits the profile of a traditional centre-forward who can press from the front.
A previous stint at Everton, where Kean scored twice in 32 Premier League appearances, counted against him for years. He has spent much of his career since trying to distance himself from that chapter.
Paris FC and Saudi side Al-Hilal have also been linked with the forward earlier this season.