The Dane has been linked with Everton.
Britton told the Daily Express: "Michael has been fantastic. He trusts the players to do their jobs and his signings have been brilliant - especially Michu, Chico and Jonathan de Guzman - and we've had a brilliant season. I just hope we can keep him.
"All the managers have done a good job at the club and moved on. It's no surprise to see Michael linked with a number of jobs, not just here but even in European football.
"But hopefully we can keep him. Continuity is very good and I'm sure he wants to build on our success in the Europa League next season.
"Kenny Jackett was the last one to leave, courtesy of the board's decision, in 2007. The others have been poached. But that shows we are doing well as a football club.
"The board always chooses the right men to succeed the previous manager, but hopefully they can have a summer off."