The 24-year-old has emerged as a potential replacement should Paul Pogba depart Old Trafford this summer.
There were widespread reports in Italy suggesting a switch was close to completion with a £90 million offer said to be on the table.
Lazio head coach Simone Inzaghi has made his stance clear on the Serbia international, he would like him to remain in Rome but understands some offers are too good to turn down.
“My thoughts are that I’d like Milinkovic-Savic to stay,” Inzaghi said. “But I also believe the club has to consider offers when they come in and then make a decision.
“Milinkovic is 24 years old now, he’s no longer a kid. I can give him advice, he is at our disposal and hasn’t missed a training session, but then I don’t know what will happen.
“I hope he stays.”
Milinkovic-Savic was touted as the ‘€100m man’ last summer and he was expected to make a move to United then, only for the transfer to fall through.
He stayed in Serie A where his form tailed off, but the physically-imposing midfielder remains a wanted man and Inzaghi is aware of the task at hand in attempting to replace such a talent.
“We know that if he was to leave, we’d have some important shoes to fill,” Inzaghi added.
“I hope he remains, he had a great pre-season training camp, but the market is open, and we are ready for any situation.
“If he were to leave, we’d need a physical player to come in the midfield. Purchases are targeted and chosen together with the club, we have sat down and talked calmly.
“If an important offer arrives, it is only right the club take it into consideration.”
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