Swansea were narrowly beaten 2-1 by Manchester United at Old Trafford at the weekend leaving the club two points clear of the bottom three.
Alan Curtis was placed in temporary charge following Monk's dismissal and has overseen a win, two draws and two narrow defeats to both Manchester sides in the last month.
Speculation continues to surround the Swansea hotseat with the likes of Brendan Rodgers, Gus Poyet and Marcelo Bielsa some of the names linked to the Liberty Stadium.
'They need to commit'
But speaking in his role as a pundit on Match of the Day, former Chelsea and Blackburn Rovers star Le Saux had his say on who he thinks should be the new manager.
"They were three unbeaten ahead of today," Le Saux said on MOTD.
"I think it's really important that they make a commitment to him (Curtis) at least until the end of the season in order for the players to then buy into what he's trying to do.
"The thing with Swansea, they play very, very well, they've got some excellent creative players but obviously they're looking vulnerable."
Massive chance for Curtis
Swansea have certainly not disgraced themselves under Curtis so far.
They may be in a worse position than when Monk left but are more points clear of the danger zone.
Curtis has a massive chance to do his job prospects the world of good next time out in the league when Swansea entertain relegation rivals Sunderland at the Liberty.
Swansea know a win in that six-pointer will put clear daylight of seven points between themselves and Sam Allardyce's side going into the last 17 games of the season.
Lose and Sunderland close the gap to just one point and Curtis will find himself under immense pressure if he does have any realistic hopes of getting the job full-time.