Former Luton boss John Still is confident they'll stay up.
Luton host Manchester United later on Sunday.
Rob Edwards is not just a terrific manager but a terrific person," he told Sky Sports.
"They deserve every plaudit that they get. When someone asked me at the start of the season whether I thought Luton would stay up. I said I hope so, but it would be tough. My answer now has changed, they will stay up.
"Did I think they'd be in the Premier League this soon? Probably not but it doesn't surprise me they are. The whole structure has been geared to it. All the people and the board of directors are the same as when I was there.
"Everyone works diligently to provide the best opportunity for the club. It was always going to go up the leagues. If you leave something behind that other people can come in and add to rather than take away and destroy, that's fantastic. I try to do that. I get a lot of plaudits for my part in getting Luton to where they are but, in my mind, I have played a part but only a small part."