The Egyptian star scored a record 32 Premier League goals to scoop the Golden Boot, while he also claimed the PFA Players' Player of the Year, FWA Footballer of the Year and the Premier League Player of the Season.
Former Liverpool midfielder Johnston, who won five league titles, the European Cup, FA Cup, League Cup and Community Shield during his time on Merseyside between 1981-88, said it is vital the club keep hold of Salah, having already lost Luis Suarez to Barcelona in 2014 and Philippe Coutinho in January.
"Liverpool have to keep Salah," the 57-year-old Australian said in an interview with Omnisport.
"You can't lose Luis Suarez, Philippe Coutinho and then lose Mo Salah.
"A lot of people in Liverpool are in love with that man, men and women, and kids and babies. We're all in love with him. If the love of our life gets dragged away to another family before we've seen them grow up properly, you get annoyed.
"Salah cannot possibly leave Liverpool."
The Reds have already signed Naby Keita from German side RB Leipzig, while more arrivals are expected on Merseyside.
And Johnston believes Liverpool – with the help of some new faces – will challenge for domestic honours in 2018-19.
Johnston said: "I'm shocked and delighted to see them in the Champions League final and I'm delighted to see them fourth in the league – 100 per cent they're on track.
"No one is leaving. This squad has to be bolstered because I think the Scouse community has had enough of people picking off our best players. Enough already.
"We're on track and the train is moving forward. We have to win as many Champions Leagues as Real Madrid."