The Egyptian forward is rated by his club boss Jurgen Klopp as the best player in the world currently, after scoring 12 goals in 11 games for the Reds this season.
His current deal runs through to the end of the 2022-2023 season, but Liverpool is eager to secure his future as soon as possible.
It is clear that in-form Salah is happy at Anfield, but there is more to it than that, with the club needing to satisfy his financial demands.
He is putting all the onus on Liverpool to come up with the attractive offer that will persuade him to make a long-term commitment, knowing there would be clubs queueing up to offer him big-money deals should he ever leave.
At the age of 29, the next contract he signs will likely be the last major deal of Salah's career.
"This doesn't depend on me. If you ask me, I would love to stay until the last day of my football [career]," Salah said.
"But I can't say much about that, it is not in my hands. It depends on what the club want.
"At the moment, I can't see myself ever playing against Liverpool. That would make me sad.
"It's hard. I don't want to talk about it, but it would make me really sad. Let's see what will happen in the future."
On Monday (AEDT), Salah is set to line up for Liverpool at Manchester United, where he scored three times in two visits last season, netting twice in an FA Cup defeat and then once late on in a 4-2 Premier League win.
No Liverpool player has ever scored in three consecutive away games against Manchester United, but Salah has netted in his past nine outings across all competitions.
It would almost be a surprise, therefore, if he failed to find the net at Old Trafford, with the fact United has failed to keep a clean sheet in its past nine home league matches another factor to consider.
Comparisons have been drawn between Salah and United forward Cristiano Ronaldo, and they will continue on SundayMonday (AEDT) with the performance of each man likely to be pivotal to the outcome.
In his first season at Liverpool, in 2017-2018, Salah broke Ronaldo's record of 31 Premier League goals in a 38-game campaign, scoring 32 times and averaging a strike every 91 minutes.
Salah's shot conversion rate of 22.22 per cent that season (from 144 attempts in total) is the best either he or Ronaldo have managed in their Premier League careers.
In terms of assists, Salah has twice reached 10 for a campaign, in 2017-2018 and Liverpool's title-winning season of 2019-2020. Ronaldo's best figure of eight was recorded in 2006-2007.
This season, Salah sits alongside Jamie Vardy on seven goals at the top of the Premier League scoring chart, heading into the weekend's fixtures.