Bayern Munich assistant manager Paul Clement and former Birmingham City boss Gary Rowett are the frontrunners to be the next Swansea City manager.
Ryan Giggs was the favourite following Bob Bradley’s exit on Tuesday, but the club are now looking elsewhere.
Wales boss Chris Coleman had been a contender but BBC Sport understands he is now out of the running.
Clement was interviewed for the job in the autumn before Bradley replaced former manager Francesco Guidolin.
The former Derby County manager, who was sacked by the Rams in February, is thought to have impressed the Swansea hierarchy, while Rowett has not taken on a job since his sacking by Birmingham City earlier in December.
It is understood discussions about filling the vacant manager’s position are now beginning, with the club hopeful of having Bradley’s replacement in place prior to the trip to Crystal Palace on 3 January.
Alan Curtis, who is taking temporary charge of the team, believes the club’s next manager should be British and have experience of the Premier League.
“It has to be the right man. Ideally they would be British and know the Premier League,” Curtis said.
“[The owners] have to be satisfied he fills all the criteria for getting us out of the trouble we find ourselves in.”