Brighton boss Gus Poyet and Blackpool's Ian Holloway had led the betting after Rodgers informed Swansea of his desire to leave and sign a three-year deal at Liverpool. The two clubs are set to agree a compensation deal on Thursday.
But a surge of bets on Jones saw the 42-year-old's odds come in as far as 1/10.
Jones worked at Swansea as Roberto Martinez's assistant before joining the Spaniard at the DW Stadium in 2009. He was approached by the Swans to take over from Paolo Sousa prior to the appointment of Rodgers in 2010.
But Press Association Sport understands Wigan have yet to receive an approach for Jones.
Reports suggest Rodgers will be taking three members of his backroom staff to Anfield, with assistant manager Colin Pascoe, analyst Chris Davies and conditioning expert Glen Driscoll all set to make the move to Merseyside.
But Swansea chairman Huw Jenkins has moved quickly, holding preliminary discussions with senior officials at the club over their pursuit of a replacement for Rodgers.
It is understood the club had started to make preparations for life without Rodgers as early as February, holding a series of meetings when he was linked with Tottenham in order to avoid being left high and dry in the event of his departure.
Poyet, Holloway, Birmingham's Chris Hughton and former Denmark international Michael Laudrup have all been linked with the vacancy at the Liberty Stadium, but it is Jones who now appears the clear favourite for the role.
Former striker Jones was a popular figure during his previous spell in south Wales, and would fit the club's desire to appoint someone willing to continue the attractive passing style that has served Swansea well, having helped Martinez implement that approach.
Source: PA
Source: PA