Lazio sporting director Igli Tare said Sergej Milinkovic-Savic and Ciro Immobile will both sign new contracts with the club next week.
Tare, speaking to Sky Sport Italia on Thursday night, when Lazio got their Europa League campaign off to a winning start by beating Apollon Limassol 2-1, said the deals will be completed soon.
"It's just a matter of days now," Tare said. "All will be signed at the start of next week. The agreements have been in place for some time now."
Milinkovic-Savic, 23, was linked with a move away in the summer amid reports a €100 million asking price that put off Manchester United and Tottenham Hotspur.
He is already contracted to Lazio until June 2022 but is expected to add a year to his deal on improved terms.
Immobile, 28, was on target on Thursday night with his ninth goal in his last 10 Europa League appearances.
He scored 29 goals in 33 Serie A games last season after scoring 23 times in 2015-16. His current contract runs until June 2021.