A home loss to Southampton , coupled with Huddersfield’s draw at Chelsea , means Swansea are almost certain to be relegated from the Premier League.
The Swans must beat Stoke while Saints lose at Manchester City with a 10-goal swing in Sunday’s final round of games to secure an unlikely survival.
Carvalhal is out of contract at the end of the season but had been in talks to remain at the Liberty Stadium.
However, it is understood the Swansea board have decided not to renew Carvalhal’s contract after a run of eight games without a win.
Former Wales striker Iwan Roberts says the decision on Carvalhal’s future is “crucial,” to Swansea’s future as they plan for life in the Championship after seven successive campaigns in the Premier League.
“Who’s going to be the manager now is the big question,” Roberts said before the news broke of Carvalhal’s imminent departure.
“There’s some big questions: the owners need to come out and answer some questions as well.
“The club has tried to do things on the cheap, bring players in on the cheap.”