Megson's future in doubt
Megson's current contract at The Hawthorns is due to expire at the end of this season, and it is believed Peace is unwilling to offer him a new one.
"I'm proud of what I've done but pride comes before a fall," admitted Megson.
"Over the past three years this club must be one of the top three in the country in terms of progress."
Megson has been in charge of Albion since March 2000 after previously managing Norwich City, Blackpool, Stockport County and Stoke City.
Meanwhile Albion defender Paul Robinson knows that this weekend's game against Liverpool will be a tough encounter for Megson's revamped side.
"You've got to have admiration for every team you play in this league," he told the club's official website.
"They've all got world-class players. But we're just concentrating on Saturday and then we'll take it from there.
"It's a hard ground to go to because their supporters get right behind them. The whole Liverpool XI are world-class players so we know it's going to be difficult.
"We've got to go there and try and get a win - three points would be lovely.
"The gaffer's made some great signings which include world-class and experienced players.
"Added to the players that were already here we've been able to build."