The Serbian midfielder was long linked with a move to the Premier League, most regularly touted as a potential Manchester United signing, although Arsenal were also interested.
A switch to England never materialised and the 28-year-old is now playing in the Saudi Pro League, moving to Al Hilal from Lazio over the summer for £34m.
Tare says things could have been different, though, with Manchester United making their interest extremely solid with an enormous bid of £85.5m.
The Albanian, who finished his playing career at Lazio in 2008 and moved into a sporting director role, says AC Milan also made an enormous bid for Milinkovic-Savic, but both offers were spurned.
‘Many things have been said about Milinkovic-Savic that are not true, from losing him as a free agent to the idea he didn’t want to stay,’ Tare told TV Play, via The Sun.
‘The only true thing is that President Claudio Lotito rejected a very important offer, worth over €100m (£85.5m), from Milan and Manchester United.
‘I don’t want to get into why the sale did not go through, as Lotito wanted to maintain a strong squad and keep the promises he had made to the coach.
‘Let us not forget that the season which was interrupted by COVID, Lazio were on the verge of winning the Scudetto.’
The former Genk player has turned out 16 times in the Saudi Pro League since moving to Al Hilal, scoring eight goals.
His team sit top of the table, seven points clear of Al Nassr, with fellow Serbia international Aleksandr Mitrovic proving prolific since his move from Fulham, netting 17 times in 17 league games.
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