Michael Laudrup is taking legal advice over his sacking by Swansea, while Glenn Hoddle has played down reports linking him with the club.
The Dane was axed on Tuesday following a poor run of form by Swansea, 12 months after leading the club to the first major trophy in their history.
The League Managers Association (LMA) is now writing to the club to ask for the reasons for his sacking.
On the day his temporary replacement, club stalwart Garry Monk, held his first press conference, Laudrup released a statement which read: "I am deeply disappointed to have been dismissed as manager of Swansea City.
"In particular, the manner in which it happened and the actions the club has taken since notifying me in the briefest of letters which gave no reasons why such hasty and final action was deemed necessary.
"I am, of course taking legal advice and the LMA have already written to the club asking for a proper explanation as to why I was summarily dismissed."
Laudrup also revealed his upset at being denied the chance to thank the players in person for their efforts under him.
He added: "The club has informed me that I cannot visit the training ground to say my farewells to the players so I do that now through this statement.
"The players have been fantastic and their contribution under the very professional guidance of my coaching staff has been absolutely fundamental to the club's recent successes. Three members of my staff have also been dismissed.
"Whilst league results have been disappointing of late, we are still 12th in the table and it is there for all to see the fine margins in the league this season in terms of points that separate 11 clubs.
"Although we have been unfortunate with injuries, I believe our league form would have improved and that we would have benefited from the forthcoming Europa League and FA Cup matches."
Swansea have picked up just six points from their last 10 matches and are two points above the relegation zone heading into this weekend's derby showdown with Cardiff.
The Swans, however, are through to the fifth round of the FA Cup, where they face Everton, and are also in the last 32 of the Europa League, with Italian side Napoli their next opponents.
Later in the day, former England boss Hoddle said he had not spoken to the Welsh club, despite media reports to the contrary.
According to zapsportz.com, the website founded by Hoddle last year, the 56-year-old will not be the club's next manager.
A story on the site said Hoddle had "neither sought nor applied for the Swansea post. And he has not been interviewed nor has he any plans to be interviewed for the job."
Hoddle has been out of football management since leaving Wolves in 2006, having previously held club positions at Swindon, Chelsea, Southampton and Tottenham.
Monk held his first training session on Wednesday and did his best to fend off some awkward questions from the press 24 hours later.
One of those related to defender Chico Flores, who was involved in a training ground bust-up with Monk last month.
The club have played down some of the more colourful accounts of the incident and Monk, a Swansea captain in all four divisions, insisted it would have no effect on his team selection.
"Chico will be involved in the squad, zero problems whatsoever," said Monk.
"We had a talk. Things have been blown up and we have had a laugh about it. He is a good man."
The 34-year-old also attempted to play down the upheaval Laudrup's exit would have on the club between now and the end of the season.
"We're all aware of what has happened this week. It has been a busy period," said Monk.
"I know the club and the players, nothing here is new to me. We've lost players and managers in the past and we've dealt with that.
"That's industry we are in. We're used to those experiences.
"I was just told 'Can you be ready to prepare the team'. I don't know what happened with manager and chairman. This is my club and that's what I'll do."
Monk admitted the full-time job would be a dream role for him, even if it meant the end of his playing days.
"My ultimate aim would be to manage the club, (but) I am not a player-manager. If I am in. I might not be seeing things elsewhere.
"If I have played my last game as a player it would mean I have done well."