Laurdup was sacked as a manager of the Welsh club on Tuesday, with club captain Garry Monk appointed his replacement ‘for the foreseeable future.’
Whilst 34-year-old Monk remains the bookmakers favourite to be given the job on a permanent basis, Bergkamp’s name stands out as the other potential candidate.
The former Dutch forward is an Arsenal legend, and became one of the Premier League’s major stars during 11 years with the Gunners, in which time he won three Premier League titles and four FA Cups.
Bergkamp has moved into coaching since hanging up his boots, firstly with the Netherlands national side, and now as assistant manager to Frank de Boer at Ajax.
Swansea chairman Huw Jenkins is thought to be an admirer of Bergkamp, and the passing game Ajax have implemented.
The bookies are offering odds of 20/1 that the 44-year-old will be installed as Laudrup’s successor.
Former Swansea assistant and current Everton number two Graeme Jones is the second favourite for the job, while former England boss Glenn Hoddle and ex-Athletic Bilboa boss Marcelo Biesla have also been linked with the job.