The Reds are reportedly hopeful of wrapping up negotiations with the Serie A outfit by the end of the week, with personal terms already said to be verbally agreed to boost the player's wages to £90,000-a-week.
Roma chairman James Palotta recently told a US radio station that there is "nothing" between the two clubs "for the moment" but indicated that a move could come to fruition by saying: "We'll see what to do."
With interest in Bayer Leverkusen's Julian Brandt cooled, Liverpool are also keeping alternative targets in mind if an agreement cannot be found to sign Salah - with Lazio winger Keita Balde thought to be among the other options.
If a deal is struck for Egyptian international Salah, it is likely to be one that succeeds the £35 million move for Andy Carroll in 2011 as the club's record transfer fee.
Roma are believed to be looking for £35 million for the 24-year-old although add-ons could see that fee increased.
Egyptian seen as ideal wide addition
Salah almost signed for Liverpool in 2014 before eventually choosing to sign for Chelsea, though an unsuccessful spell at Stamford Bridge saw him loaned to Fiorentina and Roma, before signing permanently for the capital club for £13 million last summer.
Liverpool's fee represents a clear increase on that fee, though Salah returned 19 goals and 13 assists across all competitions for the Italian side - who finished second to Juventus in the league - last season.
The Senegalese winger was a revelation in his first season at Anfield and was sorely missed when he was at the Africa Cup of Nations and later out injured.
Salah, a similar calibre of wide-man with an equally as impressive output, though like Mané - he is expected to take part in the 2019 AFCON leaving the club with a selection headache later down the line.
Another potential problem is that Salah and Mané's best performances have come from the right side of the attack, meaning one will have to be sacrificed on the left - or potentially as a No.10 - if they are to start together in the same line-up.
Should Salah become the club's most expensive player, that record could soon be broken yet again with Southampton defender Virgil van Dijk and RB Leipzig midfielder Naby Keïta both on Liverpool's radar and expected to cost a minimum of £50 million.