The 22-year-old Nigerian ace has emerged as one of Serie A’s top box-to-box stars in recent times, earning a call-up to represent his nation at the World Cup earlier this year.
Liverpool were linked with the starlet over the summer, yet their pursuit of Emre Can put manager Brendan Rodgers off.
But, the Northern Irishman is now keen to get in another central star, with Lucas Leiva attracting interest from Inter Milan.
Lazio are thought to be reluctant to let Onazi go, but the Rome giants are interested in Borini.
Rodgers is keen to use this to negotiate a deal, and is willing to hand the Stadio Olimpico side £8m as well as the struggling forward.
Borini is thought to have little future at Anfield, with his manager frustrated by the player’s decision to reject a £14m move to Sunderland during the last transfer window.
The ex-Swansea and Chelsea ace wanted to battle for his future on Merseyside, however limited playing time over the first half of the season may be enough to have altered his stance.