Sheehan was sacked as head coach on Tuesday afternoon after a poor run of recent results and performances.
Martin and Rodgers are joined at the top of the list of those tipped to take over by Kim Hellberg, the Swede currently in charge in Hammarby IF in his homeland, who has been linked with the Swans previously.
Bookmakers DragonBet currently list Hellberg as 2/1 favourite, with Rodgers, Martin and Darren O’Dea - Sheehan’s assistant until the head coach’s dismissal - all at 5/1.
Others in the frame include former Manchester United star Michael Carrick - sacked recently by Middlesbrough - as well as ex-Swans defender Alan Tate, who was a long-time assistant to Steve Cooper at various clubs.
Early outsiders for the job include big names such as Gary O’Neil, Rob Page, Slaven Bilic, and Steven Gerrard.
Sheehan’s demise followed a rapid recent decline following just a little over six months in the permanent role.
The Irish manager, who previously enjoyed what the Championship club described as “two highly impressive stints in interim charge”, was handed the job full-time towards the end of the 2024-25 campaign, following Luke Williams’ departure.
Alan Sheehan Admits Only Wins Can Save Him as Swansea City Stall Again
However, the 39-year-old has managed only four league victories from Swansea’s opening 15 fixtures this season.
“In the wake of a disappointing run, it is felt results and performances do not meet the standards expected at this stage of the season, and we have had to take this difficult decision,” a club statement said.
“The process to appoint a new head coach is already under way. We will update supporters on this process once it has been concluded.”
This disappointing start marks Swansea’s poorest league return since their relegation from the Premier League in 2018.
After a 4-1 home defeat to Ipswich Town at the Swansea.com Stadium on Saturday, the team sit 18th in the Championship table.
Swansea City owners Brett Cravatt and Jason Cohen said: “Alan has been instrumental in helping improve the club through two periods of time. Alan has a tireless work ethic, an honest approach and a positive attitude. He has put his full effort into the job on behalf of the club.
“The club would like to place on record its thanks to Alan for all of his hard work during his time at Swansea City. We wish Alan and his family all the best for the future.”
Sheehan initially joined as assistant to Michael Duff in the summer of 2023, later stepping in as caretaker boss that December after Duff’s exit.
During that first spell in charge, Swansea collected 11 points from a possible 21 before Williams was appointed in January 2024.
A year later, Sheehan found himself back in the dugout after Williams’ dismissal, guiding the Swans to a strong finish — 24 points from 13 matches — lifting them to 11th place and away from relegation danger.
Rewarded with a three-year contract in April, Sheehan was supported in the transfer market as new owners Cravatt and Cohen invested significantly to push for promotion.
Signings such as Adam Idah, Marko Stamenic, Zeidane Inoussa, and Ethan Galbraith highlighted that ambition.
Yet the promising rebuild has failed to deliver results on the pitch, with particular scrutiny aimed at the side’s lack of attacking threat.
During the Ipswich defeat, sections of supporters voiced their frustration, booing at both half-time and full-time, with chants of “we want Sheehan out” heard after the match.
Sheehan departs south Wales having won just one of his last eight games in all competitions.
After the international break, the Swans resume Championship action away at Bristol City on Saturday, 22 November.
