Jody Morris is in discussions with Swansea over the managerial vacancy at the Liberty Stadium, with MK Dons boss Russell Martin also in the frame.
Morris is keen to become a manager after working as assistant to Frank Lampard at Chelsea and Derby.
He was a successful coach in the Blues' academy before leaving to join Lampard at Pride Park in 2018.
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The 42-year-old former Chelsea and Leeds midfielder has been out of work since leaving Stamford Bridge in January.
He is in competition for the Swansea job with Martin, although it is understood that no formal discussions have taken place with the MK Dons manager.
The former Norwich defender is under contract with the League One club until next summer.
He ended his playing career to become MK Dons manager in November 2019 and helped keep the club in League One.
Martin then led the side to a 13th-place finish last season - his first full campaign in charge.
QPR assistant boss John Eustace was also under consideration but ruled himself out of the running last weekend for personal reasons.
Swansea have been looking for a new manager since Steve Cooper quit last week after two seasons in charge, both of which ended with disappointment in the play-offs.
He had one year remaining on his contract at the Liberty Stadium, but the club said: "Despite efforts by the club to enter dialogue with regards to a contract extension, it was subsequently agreed by both parties to mutually part ways ahead of the 2021-22 season."
Swansea are keen to make an appointment as soon as possible, with their Championship season kicking off away at Blackburn in 10 days' time.