The Dane was removed from his position at the Liberty Stadium on Tuesday night with the club sitting in 12th position in the Premier League table, but Laudrup has announced plans to contest the decision made by the Premier League outfit.
A statement from Laudrup issued by the League Managers Association reads: "I'm deeply disappointed to have been dismissed as manager of Swansea City, in particular with the manner in which it happened and the actions that the club have taken since notifying me in the briefest of letters, which gave no reason 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 dismissed.
"Until we receive the response, I am unable to say anymore about the termination, but I do want to take this early opportunity to thank the Swansea City fans for their continued support and to say that it has been an honour to manager this great football club."
Garry Monk has been placed in temporary charge of Swansea ahead of their clash with rivals Cardiff City at the weekend.