Swansea City 1 Stoke City 2
Carlos Carvalhal says Swansea's American owners have asked him whether he would be available to remain as manager next season.
Swansea's relegation from the Premier League was confirmed by a 2-1 home defeat to Stoke.
Reports surfaced on Thursday that Swansea would not take up the option of extending Carvalhal's short-term contract.
The 52-year-old former Sheffield Wednesday boss was appointed in December with Swansea bottom of the league and five points from safety, and he oversaw a dramatic turnaround in form before a late-season collapse ended the Welsh club's seven-season stay in the top flight.
"The news that came out this week was not real," Carvalhal said. "I spoke to the owners on Saturday and they asked me about the possibility to work the next season.
"We didn't know what would happen today, so I replied I need a little time to think.
"I will take two or three days to talk with my family, my friends and my agent.
"After that I will talk with the club again and we will make a decision, for me and for Swansea because this is a fantastic club with a good organisation.
"We must come back (to the Premier League) as soon as possible, whether it is with me or not we will see."
Swansea had needed to beat Stoke to survive, as well as seeing Southampton lose to Manchester City with a 10-goal swing in the process.
Andy King gave them faint hope that was possible, but Badou Ndiaye and Peter Crouch put Stoke ahead before half-time.