Transfer talk has surrounded the Serbia international for some time, with his reputation having been enhanced during a productive spell in the Italian capital.
At just 24 years of age, there is considered to still be plenty of potential to be unlocked in his game.
United are reported to have expressed an interest in buying into that development, with a big-money move to Old Trafford being mooted.
Another Premier League window has, however, swung shut with no deal done and Milinkovic-Savic insists he never considered a switch to be on the cards.
He told Sport Plus: “You’ll never hear me say that I want to leave Lazio.
“I never mentioned a possible transfer to Manchester United, it was just a newspaper story.
“The situation doesn’t weigh on me because I know there’s still time for a possible transfer.
“If something has to happen, it will. There hasn’t been anything until now and we’re moving forward.”
Milinkovic-Savic recenty told Serbian media outlet Espreso that he was pleased to see the latest round of rumours brought to a close.
He said: “The Premier League transfer window is shut, so the Manchester United story is finished.
“I wasn’t irritated by everything that was written in the papers, because my mind was concentrated on preparing for the new season in the best possible way.
“I am where I am and I want for nothing at Lazio.
“I don’t think much about the transfer market. All sorts of things were written about me, but I know where my mind is and who I have a contract with.”
Lazio have Milinkovic-Savic tied to a long-term contract through to the end of the 2022-23 season.
With that deal in place they are under no pressure to sell, but club president Claudio Lotito conceded earlier this summer that there may come a day when his hand is forced.
He said when quizzed on a prized asset: “If an important offer arrives, it is only right the club take it into consideration.”
Windows are still open across Europe, but there will be no approaches from the Premier League to fend off until at least January as English top flight clubs have seen their market shut down for 2019.