Serbia's 2-0 defeat to Brazil on Wednesday night saw the White Eagles exit the competition in the group stages.
Milinkovic-Savic scored 14 times and provided nine assists during an impressive 2017-18 campaign with Lazio, and a number of clubs - including Manchester United and Real Madrid - have been linked with his services.
The 23-year-old, however, has said that he "would be happy" to remain at Lazio beyond the end of this summer's transfer window.
"I need a little bit of rest now," Milinkovic-Savic told Mediaset. "I'll return to Rome and I would be happy if I stay at Lazio, as I'm content there and I have a contract.
"I read something different in the papers every day, but I haven't thought about it yet. First I'll rest for a bit, then we'll see."
Lazio are believed to want in excess of £100m for the powerful midfielder this summer.