Milinkovic-Savic and Tadic were part of Serbia's opening-game win over Costa Rica on Sunday, but it was the captain Aleksandar Kolarov who secured the 1-0 victory with a stunning free-kick.
Lazio are aware of interest in Milinkovic-Savic and have valued him at more than €90 million (£79m/$104m), leading to the 23-year-old to be called "the €100m man."
Southampton midfielder Tadic is five years the senior of Milinkovic-Savic, and has been impressed with how the emerging star, who has also been linked with Real Madrid and Juventus, has handled the limelight.
"He is a good player, he is young," Tadic told Goal in Samara. "He can learn a lot of things but he has a big talent. He has the capacity to go far. That's it. He is the future of Serbian football.
"I say to him to just be calm and work smart and he does.
"He needs to work for his team and then after he can show his qualities. I think he is a clever guy. He is a good boy and he just needs to keep his head calm [due to ongoing rumours]. There is a big future for him."
Serbia's win on Sunday was vital for them in Group E, with tougher games against Switzerland and then Brazil to come.
Tadic says that, despite Brazil's opening-game draw with Switzerland, the Selecao will almost certainly advance to the round of 16, making Serbia's upcoming game against the Swiss a possible decider for qualification to the knockout stages.
"Yes, it is probably going to be like that. Brazil [and] one other," the Southampton man said. "They are one of the favourites for the title. One more team as well as them will probably go through.
"Normally when we play against Brazil, we will just try to stop them from winning. We will see, it is difficult to beat everybody, not just Brazil. I think we are a good team but the problem is that sometimes we need to be more smart. More intelligent, more experienced.
"We showed that today ... We need to show it in the next game also. Before the Costa Rica game, we said this was the biggest game but now we say the next is biggest. We have to go step by step, it is as simple as that."
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Tadic came into the World Cup having put in some big performances to help Saints survive the threat of relegation from the Premier League.
"It was a very important achievement," Tadic said. "It was a tough time. It was difficult but this was the first time that I was in this kind of situation.
"I am happy because Southampton is a huge club and shouldn't go down."
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