Swansea chairman Huw Jenkins says it is “vital” the club appoint “the right person” as Carlos Carvalhal’s managerial successor.
Swansea have announced that they will not be extending Carvalhal’s contract.
The Swans were relegated from the Premier League on Sunday, the end of their seven-year stay in the top flight confirmed by a 2-1 home defeat to Stoke.
Carvalhal was appointed as Paul Clement’s successor in December, just three days after leaving Sheffield Wednesday.
He won five of his first nine league games as Swansea climbed to 13th place, but they were condemned to the Sky Bet Championship after picking up only three points from the last 27 on offer.
Managers already being linked with the post include former Wales boss Chris Coleman, who was recently sacked by Sunderland, and Swedish club FK Ostersunds’ boss Graham Potter, while long-serving Swans player Leon Britton also has his admirers.
Jenkins said: “While there are already rumours linking us with several managers, it is vital that we identify the right person to take this team forward.
“We’d like to put on record our thanks to Carlos for his enthusiasm, hard work and commitment since arriving at the club in December.
“Naturally, we are all disappointed with the club’s relegation from the Premier League, and following discussions with Carlos, we felt it was in the best interests of both parties that we move in a new direction.
“We will now be looking to appoint a new manager in readiness for the 2018-19 season.”
Carvalhal said after the Stoke game that Swansea’s American owners had spoken to him about being in charge next season.
But Swansea have decided not to take up the option of extending the Portuguese’s short-term contract.
Carvalhal said: “First of all, I must thank the chairman Huw Jenkins and majority owners Stephen Kaplan and Jason Levien for their full support.
“From the players to the chefs, the physios and staff, I really enjoyed working with you all.
“I also appreciate the way the press at local and national level treated me. I like to think we had a very positive relationship.
“But most of all, I must thank the supporters. They were absolutely fantastic during my time here, and they follow the team up and down the country with huge passion. You should be very proud of your support.
“While Swansea and myself will go in a different direction, I wish the club all the best. I am sure I will be a Jack forever.”