During a highly successful eight-year spell with the Biancocelesti, Milinkovic-Savic earned a reputation as one of Europe's finest goalscoring midfielders and was persistently linked with a move to the Premier League.
The 28-year-old managed 69 goals and 59 assists in 341 matches for Lazio, who signed him from Genk for €12m (£10.3m) in 2015, while he also won one Coppa Italia and two Supercoppa Italianas while on the books at Stadio Olimpico.
All of Arsenal, Chelsea and Liverpool were all believed to be keen on bringing the Serbia international to England, but he was ultimately seduced by Middle Eastern riches, joining Al-Hilal in a €40m (£34.2m) transaction.
Milinkovic-Savic followed Neymar, Aleksandar Mitrovic, Ruben Neves, Kalidou Koulibaly and Bono to Al-Hilal, where he has hit the ground running with nine goals and five assists from 22 matches across all tournaments.
Jorge Jesus's side are the favourites for the Saudi Pro League title as they sit seven points clear of Al-Nassr at the top of the table, and Milinkovic-Savic is under contract with the club until the summer of 2026.
However, during a revealing interview with Tuttomercatoweb, ex-Lazio director Tare, who was in the Biancocelesti offices from 2008 to 2023, confirmed that both Man United and AC Milan came forward with mammoth bids for the midfielder.
Club president Claudio Lotito turned both offers down, though, and he denied claims that Milinkovic-Savic was actively pushing to leave the club during his final season.
"Many untrue things have been said about Milinkovic-Savic, from his farewell on a free transfer to the fact that he didn't want to stay, the only true thing is that Lotito rejected a very important offer, worth over 100 million euros, from Milan and Manchester United," Tare said.
"I don't want to say too much about the lack of sale, even if there was a question of budgets, but Lotito's choices were to maintain a strong team and respect the promises made to the coach. Let's not forget that in the year of Covid, Lazio was about to win the Scudetto."
With Milinkovic-Savic Saudi Arabia-bound, Man United captured Mason Mount from Chelsea to bolster their midfield ranks, but the 25-year-old's first season at Old Trafford has not gone to plan.
Mount has only recorded one assist from his first 12 matches for the Red Devils, and he has been sidelined since the November international break with a serious calf injury.
While a big-name striker and defensive reinforcements may take priority this summer, there could be scope for a new midfielder to arrive if a couple of unwanted players depart the Theatre of Dreams on permanent deals.
Donny van de Beek - currently on loan at Eintracht Frankfurt - should be one of the first names out of the door, while Sir Jim Ratcliffe is supposedly prepared to part ways with Casemiro, who is a target of Al-Nassr.
The Brazilian recently played down talk of a possible exit from the club, though, insisting that he is "so happy" at Old Trafford despite his struggles in the 2023-24 season.