Willis believes England's selectors must "send a message out" before the Boxing Day Test in Melbourne and pin-pointed Swann and Prior, as well as opener Michael Carberry, as the players to make way.
Off-spinner Swann has come in for punishment from an Australian side intent on attacking him to the tune of 80 runs for each of his seven wickets, while wicketkeeper Prior has been well below his best with bat and gloves.
"Graeme Swann should be sacked. No doubt about that," Willis said on Sky Sports' 'The Verdict' programme on Tuesday night.
"You can't keep playing Swann, his wickets are costing 90. All the right-handers have got the wood over him. You've got to give Monty (Panesar) a go."
Speaking of Prior, he added: "I'd like to send a message out to some of the players.
"I'd make more than one change. He (Prior) wouldn't be the only one to go.
"I don't think Michael Carberry, in the long term, is a good enough player to play Test cricket.
"His age is against him as well. We are all hearing in the long term Joe Root is going to be Alastair Cook's opening partner so get him back up there and open."
In naming a starting XI for the MCG, Willis also included a debut for Yorkshire batsman Gary Ballance, adding: "So a few changes going into the Melbourne Test match, a breath of fresh air, but if I'm brutally honest I think they are going to lose this series 5-0."
Former England opener Geoffrey Boycott was equally as forthcoming saying Cook's side had "cocked it up big time".
Boycott told BBC Radio 5 Live: "The planning and the prep of the team - it's all gone haywire. In all areas they have been better than us.
"They have had good plans and executed them really well while we've cocked it up big time."
Boycott was particularly critical of England's coaching staff and has demanded team director Andy Flower leave his position if he is not up to the challenge of leading the side any more.
"Some of our coaching staff should have a serious look at themselves because we are on the down and Australia are on the up," added Boycott, who scored 8114 runs in 108 Tests for England.
"We should be thinking and planning for 2015. Is our coach up to it?
"The top people have to decide - Andy Flower, are you going to be here next year? Are you staying or going? If you've had enough, go now.
"We have to be up for the challenge - we have to have the balls to do something."