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 on Sunday 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.
"They said they want to talk to me and that makes me very proud."
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 during a strong start, but Badou Ndiaye and Peter Crouch put Stoke ahead before half-time.
And Carvalhal said Swansea's demise was down to their miserable first half of the season when his predecessor Paul Clement claimed only 13 points from 20 games.
"We pushed a lot, we did 18 games and got 20 points," said Carvalhal, whose side ended the season without a win in nine.
"We achieved more points in this time than Stoke, Southampton, Huddersfield, West Brom and Bournemouth and the same as Leicester.
"I think the few points we did in the first 20 games - just 13 - made it difficult to recover and achieve a better position.
"We deserved more against Everton and Chelsea, we got nothing and they were crucial."