Hoddle is understood to be interested in the position, and is set to be interviewed by Swans chairman Huw Jenkins this week.
Hoddle was reportedly sounded out about the possibility of taking over the Welsh club three months ago, but was reluctant to get involved whilst Laudrup remained in charge.
The 56-year-old has not worked in the Premier League since being sacked by Tottenham in 2003, and has not managed at all since leaving then-Championship club Wolves in the summer of 2006.
Hoddle remains keen to get back into top-flight management, and is a genuine contender for the job following the sacking of Laudrup earlier in the week.
His CV remains impressive, having managed the likes of Chelsea, Tottenham, Southampton and the England national team.
Jenkins has given veteran defender Garry Monk a chance to prove his credentials for the job in a role as caretaker boss, but the 34-year-old is not seen as the long term solution.
Monk’s appointment may not be seen as positive in some parts of the Swansea dressing room, after he was involved in a training ground bust up with Spanish defender Chico Flores last month.