Swansea hope to appoint Brendan Rodgers' successor by the end of the week, Press Association Sport understands.
The south Wales club have been searching for a new manager since Rodgers took over at Liverpool two weeks ago.
Chairman Huw Jenkins has played his cards close to his chest in the search for a new boss, but the hunt is set to be stepped up when he returns from holiday in the coming days.
A number of names have been linked with the job at the Liberty Stadium including Gus Poyet, Marcel Desailly, Dennis Bergkamp and Graeme Jones.
Wigan assistant manager Jones was the early favourite for the job and held talks over the position, but he appears to have fallen down the pecking order due to his reservations about taking his first managerial role, while Desailly has revealed he turned down an approach as he did not feel the timing was right.
Instead it is former Real Madrid and Barcelona midfielder Michael Laudrup who is the odds-on favourite to take over at the Barclays Premier League club, and it is understood that the Dane has held talks over becoming Swans' boss.
Swansea are keen for their new manager to embrace the passing philosophy adopted by the club under Roberto Martinez, Paolo Sousa and Rodgers, and Laudrup would fit that mould having produced enterprising, attacking football during his spells at Brondby, Getafe, Spartak Moscow and Real Mallorca.
Blackpool boss Ian Holloway is the other leading candidate for the role, although the Seasiders have denied receiving any approach for the 49-year-old.
Holloway guided Blackpool to another play-off final last season, but having failed to return to the top flight he has admitted he would be interested in a move to a Premier League club and is a known admirer of Swansea.
While Swansea close in on a new manager, the club's hopes of completing the signing of Gylfi Sigurdsson appear to be over.
Swansea had agreed a £6.8million fee with Hoffenheim for the Iceland midfielder, who scored seven goals in 17 appearances during his loan spell in south Wales, as well as personal terms.
But Rodgers' exit for Anfield led Sigurdsson to admit he had reservations about making a permanent switch to the Liberty Stadium.
And it is understood that the deal will not go ahead, which will alert Rodgers, who has admitted an interest in signing the former Reading man should he not complete his move to Swansea.