Wigan Athletic assistant manager Graeme Jones withdrew from the running for the Swansea City manager's job last week.
The Daily Star says Jones, who spent time at Swansea when Roberto Martinez was manager there, told the Swans hierarchy that he did not see himself as a manager, and was happy with his role at Wigan.
Swansea chairman Huw Jenkins planned to appoint a new manager before going on holiday next week, but after Jones turning the job down, the search looks set to go on a little longer.