The Dudley-born chief takes his Baggies side to Burnley today looking for a win that he hopes will kick-start a great escape.
Albion, Fulham and Sheffield United are all currently rooted in the bottom three with the odds stacked against them they they will stay in the Premier League.
Allardyce signed an 18-month deal to become Baggies boss back in December although it is understood there is a break-clause in the contract that comes into force at the end of the season.
Wilder and Parker, meanwhile, have done impressive jobs at their respective clubs with Wilder guiding Sheffield United from League One into the Premier League, while Parker won promotion with Fulham from the Championship last year.
Asked about the future of relegation-threatened bosses, Allardyce said: "Sheffield United should definitely stick with Chris Wilder, if they get relegated, because of what he’s done at that football club and where he’s taken then from and to.
"He deserves the opportunity – this is his first bad season ever at Sheffield United, after five or six seasons.
"He’s taken them out the doldrums of League One and put them in a place they’ve not been for many, many years.
"They were one of the first teams from Yorkshire back in the Premier League for many, many years. You’ve got to give him full credit for that.
"A bit like Sean (Dyche) at Burnley, who went down, came back up, and he stayed.
"It’s happened here at West Brom in the past, where they’ve gone down, stuck with their manager (Gary Megson), and they’ve come back and sustained quite a long period of Premier League status
"Fulham should be the same for Scott (Parker).
"I don’t know what will happen to me — I can’t say that yet.
"But hopefully I’ll be smiling at the end of the season. As difficult as it looks, it's still my desire be sat here next season saying 'wow – how did we do that?' I’m still optimistic we can give it a go."