By SABC Sport
8th August 2023
After their initial two offers of £34million plus £4m and £42m were turned down, the Reds returned with a proposal worth £46m but that too has been rejected, the PA news agency understands.
Saints are understood to be looking for £50m for a player who has made just 29 Premier League appearances in one top-flight season.
Negotiations are expected to continue between the two sides.
Mohamed Salah's agent, meanwhile, has dismissed speculation linking the forward with a move to Saudi Arabia as the 31-year-old "remains committed" to the club.
A report in the Middle East claimed talks were taking place between the Egypt international's representatives and Al-Ittihad about a deal said to be worth around £155million over two years to the player.
Salah's former team-mate Fabinho has already made the move to Al-Ittihad this summer in a £40m transfer.
In that context the £60m fee being touted for Salah - who has scored 139 goals in 231 Premier League appearances - appeared to under-value a player who is only 12 months into a three-year deal which is the most lucrative contract in Liverpool's history.
And Salah's representative insists the former Chelsea and Roma forward has no intention of leaving Anfield in any case.
"If we considered leaving LFC this year, we wouldn't have renewed the contract last summer. Mohamed remains committed to LFC," Salah's agent Ramy Abbas posted on Twitter.
Salah scored and provided an assist for Diogo Jota while Luis Diaz also netted a brilliant, audacious volley as Liverpool beat Darmstadt 3-1 in their final warm-up at Preston's Deepdale - chosen because work is continuing on the Anfield Road redevelopment - before their Premier League opener at Chelsea on Sunday.
Jurgen Klopp fielded a starting XI which is likely to be the one which features at Stamford Bridge, with £35m summer signing Alexis Mac Allister playing the midfield holding role with no genuine contenders to fill the position following the departures of Jordan Henderson and Fabinho to Saudi Arabia.
The Liverpool manager admits he will have to find a quick fix for the weekend which is unlikely to be a long-term solution.
"In the next six days we have to find a formation for Chelsea and not for the whole season," he said.
Klopp accepts Mac Allister as the number six is far from ideal but he may have to be the man asked to fill in despite him doing his best work, both in his short time at the club and previously for Brighton, further forward.
Klopp said: "He's a top-class player with and without the ball. In a compact formation, Alexis can play there, if it's open should he play there? No. But he showed he is a brilliant footballer and has done really well."