The Red Devils have been linked with the 24-year-old as they look to overhaul their squad.
Ole Gunnar Solskjaer has already signed Daniel James and Aaron Wan-Bissaka this summer but is looking to make more additions.
And Manchester United fans have responded to a video of Matic posted on their Twitter feed telling the Serbian to help seal a swoop for Milinkovic-Savic.
Ed Woodward and co. have been linked with Bruno Fernandes as well but supporters were quick to ask Milinkovic-Savic to join Solskjaer instead.
One tweeted in response: “Sign his mate, Sergej.”
Another added: “Should do us a favour by inviting over Milinkovic.”
“SMS and Milenkovic next,” a third explained.
And Sky Sports reporter Anton Toloui believes Milinkovic-Savic is ideally suited to English football.
“I can’t think of a high-profile midfielder better suited to the Premier League,” Toloui said.
“He’s six-foot three, he’s physical, he’s got great stamina. But his range of passing is absolutely superb.
“He’s kind of the complete midfielder really. Now, the interesting thing is he’s been on Manchester United’s radar for a while.
“He was on one of a long list of targets under Jose Mourinho last summer. He’s had a fantastic season two years ago at Lazio and then last season was a bit of a down season for him.
“He was very much on the verge of a move to Juventus last summer, as ironically a potential replacement for Paul Pogba because they were still looking to fill that void from when he left.
“That didn’t happen and the player was left in a little it of limbo, took a little while to get back to his best form.
“He finished the season quite well and I can see why clubs in the Premier League are looking at a player like Milinkovic-Savic.”
United’s first pre-season match takes place against Perth Glory at midday UK time on Saturday.
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