The 28-year-old midfielder has a year left on his contract with Lazio and has been tipped to leave the Serie A giants this summer.
A move to the Premier League has been mooted with West Ham believed to be interested in signing him.
David Moyes wants a commanding presence to replace Declan Rice and the Serbian has been linked with a move to the Hammers.
But according to Spanish outlet Relevo, the midfielder’s preference is to stay in Italy beyond the summer.
He has decided against signing a new contract at Lazio and is open to a move in the ongoing transfer window.
But he is not keen to leave Italy even if he decides to move on from the Stadio Olimpico.
Milenkovic-Savic has suitors in Serie A where Juventus are believed to be interested in him.
It remains to be seen whether West Ham act on their interest and try to convince the Serbian to change his mind.
