The move comes as Tottenham grapple with an injury crisis that has left their defence severely depleted.
This season, injuries have hit Tottenham hard, with key defenders like Cristian Romero, Micky van de Ven, Ben Davies, and Destiny Udogie all spending time on the sidelines.
This has forced the club to rely on 18-year-old midfielder Archie Gray, who has had to play out of position in defence.
The situation worsened when Radu Dragusin, who had just returned from injury, picked up another knock during a Europa League match against Elfsborg.
Transfer expert Fraser Fletcher reported on X, "Spurs now in advanced talks for Fikayo Tomori. Deal worth around 25 million pounds (including add-ons) at advanced stage with Milan. #THFC @TEAMtalk." Despite the negotiations progressing well, Tomori's personal agreement is still pending.
Postecoglou, after the game against Elfsborg, commented on Dragusin's injury, "We've got to let it settle down. We'll get some more information over the weekend. He's unlikely to be involved this weekend, at the moment. We'll have to wait to see the extent of it.
"Hard to tell (the extent of the injury). It's a knee (issue), (but we've) got to let it settle down. Always a concern when it's a knee injury, but we have to wait and see."
Tomori, who played a pivotal role in Milan's Serie A triumph in 2022, has seen his playing time diminish this season. However, he remains committed to his current club, stating, "I'm always available to play wherever the coach wants me, we spoke yesterday about my role: what I have to do, where I have to be.
"I'm excited, as always I will do everything for the team."
In related transfer news, Tottenham's pursuit of Bayern Munich's Mathys Tel has hit a snag as the young forward reportedly turned down a move to the club despite an agreed 50 million pounds deal.
This has redirected Tottenham's attention towards possibly signing AC Milan's Noah Okafor, who is now on the market after RB Leipzig's interest fizzled out.
Meanwhile, Southampton have made it clear they intend to keep Tyler Dibling, another player linked with Tottenham, until at least the end of the season.
With the transfer window closing soon, Tottenham are looking to bolster their squad, particularly in defence, to navigate the remainder of the season amidst their injury woes.