It emerged this week that the Welsh outfit had severed ties with Tutumlu following a dispute over transfer policy and there has been doubt over whether or not Laudrup will remain as manager.
Laudrup says his intention is to stay, though, and Tutumlu has also now emphasised that the 48-year-old will not be leaving.
Tutumlu claims there is only an issue between himself and Swans chairman Huw Jenkins.
"There is no problem with Michael Laudrup and Swansea City," said Tutumlu, quoted by the BBC. "He is staying. It is my problem, my problem with Huw Jenkins."
- Michael Laudrup