Zaha, 27, was heavily linked with a move away from Selhurst Park last summer after handing in a transfer request.
A move never materialised, however, and Zaha remains in south London for the time being, scoring the winner in their opening-day victory over Southampton on Saturday.
Liverpool boast one of the best and most prolific attacking lines in world football with Salah, Firmino and Mane thriving at Anfield over the last few seasons.
Republic of Ireland legend Cascarino still believes the trio would benefit from more competition, however, and says Zaha would be a ‘perfect’ signing for Liverpool.
‘It is difficult to see where Wilfried Zaha could go,’ he told The Times. ‘I think he would be perfect for Liverpool.
‘He would put pressure on the frontline trio of Sadio Mane, Mohamed Salah and Roberto Firmino, but the champions are unlikely to want to pay for a back-up player the kind of fee Palace are demanding.
‘Should Zaha remain at Selhurst Park beyond the October deadline, Hodgson will need to summon all of his managerial experience to ensure he remains committed to the cause.
‘Zaha will soon be 28, and there are some Palace fans who would not begrudge him a move to a club that can compete for trophies.
‘Equally, they will grow frustrated if he stays and the performances he produced, post lockdown, return.’
Cascarino added: ‘The transfer window is open and it is no coincidence that Wilfried Zaha looks back to his swashbuckling, matchwinning best.
ar that Zaha still believes his future lies elsewhere.
‘Hodgson has done an excellent job of managing Zaha since he made clear his intentions to leave.
‘The transfer deadline is not until October 5 and, until then, one would expect Zaha to put in the kind of performances that will keep him in the shop window.
‘But what if he does not get his move by then?’
Following their stunning title triumph last season, Liverpool have endured a subdued summer transfer window, only bolstering Klopp’s squad with the signing of Greek defender Kostas Tsimikas.
The Reds made a winning start to their title defence, beating newly-promoted Leeds United 4-3 at Anfield thanks to Salah’s third Premier League hat-trick.