The United faithful are split in terms of how they feel about their assistant manager's career path.
Monk led Swansea to their best-ever Premier League season last term but a poor run of form this time around, where no upturn in fortunes seemed forthcoming, cost him the hot seat at the Liberty Stadium.
Since the announcement of his departure, a number of names have been linked with the Swans. Some have been more bizarre than others, with Sky Sports even reporting that the Welsh outfit are interested in Avram Grant!
But the latest coach to be linked with Swansea is Manchester United legend Giggs, who is currently Louis van Gaal's no.2 at Old Trafford.
Reaction has been mixed among the United faithful. Indeed, some fans can't envisage Giggs leaving the club and want the Welshman to remain in Manchester.
Others, though, feel the 42-year-old would be better off leaving - if only to ensure he can succeed as Manchester United manager some years down the line.
There is a distinct feeling that Giggs needs managerial experience of his own - and that he needs to get away from Van Gaal...
I think Giggs should take the opportunity an manage Swansea. #MUFC— (@Shaaiiibiola_) December 11, 2015
Why on earth would Giggs go to Swansea ? He is needed more than ever in his club , i really don't think he would even consider it #MUFC— Mohamed.Badri (@hunterutd626) December 11, 2015
MUFC (@sani_atk) December 11, 2015
If Swansea Ryan Giggs as manager I think he needs to jump at the chance. This is the only way he will get the experience to manage #MUFC— Manchester United (@MUFC_today) December 11, 2015
I half want Giggs to take the Swansea job, it would be good for him. #MUFC— Luis Peroda (@LuisPeroda20) December 11, 2015
If the rumours are true Ryan Giggs should definitely take the job at Swansea ! It would be a great opportunity to show #MUFC what he can do— United we are (@OliverOac8) December 11, 2015