Liverpool can expect to pay a club record fee for the 25-year-old, who is due to arrive in Merseyside to undergo a medical this week, according to multiple media reports in Britain and Italy.
Salah joined Roma from Chelsea for £12m in 2016 after a successful loan spell in Italy and the London club negotiated a sell-on clause in his contract worth 10 percent of the profit on any future sale, the Times said.
With Liverpool looking increasingly likely to break their transfer record of the £35m they paid to lure striker Andy Carroll from Newcastle United in 2011, Chelsea will make a healthy profit.
Salah scored 15 league goals for Roma last season as they finished second in Serie A and has been identified as a key signing by Liverpool manager Jurgen Klopp, whose only other established wide player is Senegal international Sadio Mane.