Laudrup has said that he would like to stay at Swansea, and the 30-year-old midfielder hopes that the team can move forward now.
"From a player's point of view, we hope he stays, and I'm sure all the supporters do too," Britton told BBC Sport.
"I think we were expecting a quiet summer with maybe a few signings, and that would be it. There's been so much speculation about the manager this summer, but the manager's come out on a few occasions and said he's going to be here next season.
"Hopefully that gets put to bed and the manager will come back on July 2 and we can knuckle down and train hard preparing for the new season."
Swansea begin their season against Manchester United on August 17.