Speaking ahead of the lead-up before the two clubs' do-or-die Third Round FA Cup clash, the two ex-Premier League players, who have three FA Cup winner's medals between them, were both of the opinion that the tie could mean the end of Hodgson's reign at Anfield, should they lose badly to the Red Devils.
Speaking at the ESPN STAR Sports studios to reporters, McMahon said: "Hodgson clearly can't afford to tinker and save players for such an important fixture, especially against Liverpool's bitter rivals."
"He (Hodgson) has everything to lose- if he wasn't facing the sack (after their 3-1 loss to Blackburn) he certainly will if they lose to Manchester United", the ex-Liverpool captain added.
Ex-Manchester United player Parker was in agreement, but believes that even if Liverpool beat the Red Devils, their victory would not guarantee that Hodgson's future will be secure.
"Everyone thought that when Liverpool beat Chelsea it would be a turning point for Hodgson's side", Parker said.
"There's just been too many blips this season at Anfield, and it's really not about who they beat anymore, but whether Liverpool can actually get a run of wins going in order to get some momentum", he added.
According to McMahon, the result would depend much on "which Fernando Torres showed up".
"Torres can turn it on when he wants to, and he has always given Nemanja Vidic a torrid time", the ex-Liverpool player declared.
"The question is, which Torres turns up?
" If it's the Torres of this season- with a body language that shows he doesn't want to be around- then this game will be easy for Manchester United!"
Paul Konchesky could very well have to contend with an in-form Nani if Sir Alex Ferguson decides to play him, and Parker believes that the Portuguese could prove too hot to handle for the Liverpool defender.
"Nani has been the most consistent wide player in the Barclays Premier League this season, and Konchesky is simply an average player, and simply not good enough for Liverpool", Parker said.
McMahon also believes that the state of mind of the Liverpool players could prove crucial in determining how the FA Cup tie would swing, saying: " They (Liverpool players) will be distraught, and if United score an early goal Liverpool could be in for a hiding!"
With the question on everyone's lips about Roy Hodgson's future, both players were asked who they thought would be good to take over at Anfield.
Interestingly enough, McMahon believes Jurgen Klinsmann would be a good fit for the Merseysiders.
"Klinsmann, for me, has got bright ideas, and what's more, has a wealth of knowledge about the game, especially with his connection with German football and the young talent in the country", he said.
"What Liverpool need is a manager who's young, fresh, exciting, and is knowledgable about European football", McMahon added.
Parker agreed, adding: " The next manager will need to be able to make changes without ruffling too many feathers ,not like Graeme Souness. That will buy him some time to improve the side while maintaining momentum."
When asked by reporters, both ex-players pointed to a Manchester United victory, with Parker plumping for a 2-0 win for the Red Devils, and McMahon deciding on a 3-0 scoreline to Ferguson's men.