The 18-year-old - who came through the Dogues academy ranks - is already a key player for Paulo Fonseca, registering three goals and one assist in 37 first-team appearances.
All three of Yoro's efforts for Lille have come during a breakthrough 2023-24 campaign, in which he has made 15 starts in Ligue 1 and a further three in the Europa Conference League.
Lille went through their Conference League group-stage campaign unbeaten thanks to the efforts of Yoro, an aerially dominant defender at 6ft 3in tall, and he has also earned four caps for France's Under-21s.
Yoro was only promoted to Lille's senior ranks in 2022, and his first professional contract with Les Dogues only has another 18 months left to run, leaving the Ligue 1 side at risk of losing their prospect in the near future.
With Lille potentially being pressured into a sale this summer if the teenager refuses to sign a new contract, all of Man United, Man City and Chelsea are said to have registered their interest in a deal for Yoro.
However, Chelsea are currently said to be prioritising attacking additions, and in an attempt to steal a march on the Blues, Le 10 Sport claims that Man United and Man City have now touched base with Lille.
The Red Devils are particularly keen to bolster their defensive ranks in 2024, as Jonny Evans and Raphael Varane are both now in the final six months of their contracts, while Harry Maguire, Victor Lindelof and Lisandro Martinez have all been plagued by injuries this season.
Head coach Erik ten Hag reportedly wants Evans to be handed a new one-year agreement, but Man United decided against triggering a 12-month extension in Varane's deal, leading to the Frenchman feeling like he is being forced out.
Meanwhile, Man City reinforced their backline over the summer with the capture of the highly-rated Josko Gvardiol from RB Leipzig, but another youthful addition could be sought amid John Stones's perennial injury problems.
Despite Yoro's uncertain contract situation, though, Lille president Olivier Letang has reportedly slapped an extortionate price tag of €90m (£78.1m) on the defender's head, which no party would be expected to fork out during the January window.
However, Letang will be forced to relent if Yoro shows no desire of penning a new deal at the Groupama Stadium, and both Liverpool and Paris Saint-Germain are also attentive to the situation.
PSG have already bolstered their backline in the opening hours of the January transfer window, though, signing 20-year-old Lucas Beraldo from Sao Paulo, who was also linked with a move to Liverpool.
The Reds may seek out a new defender in January following Joel Matip's season-ending ACL injury, but Fluminense's Nino - whom they have allegedly enquired about - could prove to be a far cheaper acquisition than Yoro.