Monk, once considered a candidate for the England post, was axed by the South Wales club having presided over just one victory since August, with Swansea sitting 15th in the Barclays Premier League, but only one point above the relegation zone.
Here, Press Association Sport assesses some of the names the Swans could consider to be Monk's replacement.
BRENDAN RODGERS
The Northern Irishman would be a hugely popular choice with the Swansea faithful as he took the club into the Barclays Premier League in 2011 before joining Liverpool the following year
He came close to winning the title at Liverpool in the 2012-13 season, but left the club in October after more than three years at Anfield
Rodgers is currently out of work, but has spoken of his desire to get back into management and he knows the set-up at the Liberty Stadium well and has emerged as the early favourite with bookmakers.
DAVID MOYES
Moyes spent over a decade at Everton where he won universal praise and the League Managers' Association annual award three times
But his time at Manchester United turned sour and he left 10 months after being appointed Sir Alex Ferguson's successor, while a Spanish sojourn at Real Sociedad lasted just under a year
The Scot has said he will consider his next position carefully, but his record on Merseyside - and before that at Preston - still makes him an attractive proposition.
MARK WARBURTON
The current Rangers manager has a Sky Bet League One promotion on his CV at Brentford in 2014 and guided the London club into the Championship play-offs the following season before a difference over the management structure at Griffin Park with Bees owner Matthew Benham saw him leave and eventually head north
Warburton is on course to lead the Gers back to the Scottish top flight, but could consider a more challenging return south of the border.
GRAEME JONES
The former Swansea number two has been linked with the top job at the Liberty in the past
He followed Roberto Martinez to Wigan and Everton, where his work on the training ground has impressed
Jones is known to get on well with members of the Swansea hierarchy and at 45 years of age the time could be right for him to step out of Martinez's shadow and make the move from assistant manager to being the boss.
ROBERTO DI MATTEO
Di Matteo has a Champions League winners' medal from his eight-month spell at Chelsea in 2012, while he was most recently at German giants Schalke before leaving in May
The former Italy international cut his managerial teeth at MK Dons and then West Brom, while his success on a smaller budget will not have gone unnoticed with the power-brokers at Swansea
Source : PA
Source: PA