The 23-year-old has emerged as one of the most sought-after talents in European football on the back of an impressive three years in Serie A.
In the end, Lazio’s reluctance to sell amid talk of a €100 million (£89m/$118m) asking price led to Milinkovic-Savic staying put.
He is now ready to cement his standing in the Italian capital by extending a deal already due to run until 2022.
Lazio are also expecting Ciro Immobile to prolong his stay, with the necessary paperwork in place for two important agreements.
"All will be signed at the start of next week. The agreements have been in place for some time now."
Milinkovc-Savic joined Lazio from Genk in the summer of 2015.
He has now taken in 126 appearances for the club and scored 25 goals.
He was among the goals again in his most recent appearance, as Lazio opened their 2018-19 Europa League campaign with a 2-1 victory over Apollon Limassol.