"I will try to stabilise the club because I wish to be here for a long time," the 52-year-old Carvalhal told the club's website. (www.swanseacity.com)
"We stayed for two-and-a-half years at Sheffield Wednesday. In the Championship, the average (length of reign) for a manager is six or eight months... I am confident myself and my staff can help the club to a better position... my future isn't a problem.
"I don't worry about a paper contract. You have to prove yourself day by day, to the fans and the media and the club and the players. After that, things will come naturally."
Carvalhal, who has worked at 15 clubs, is set to name a four-member support team with two coaches and two analysts, and is also considering a role for interim player-coach Leon Britton.
Midfielder Britton guided Swansea to a 1-1 home draw with Crystal Palace before suffering a 5-0 thrashing at Liverpool in his two games in charge following Paul Clement's dismissal.
"I am sure he deserves a lot of respect from the club and we will consider the importance he has in the club. Let's see in which position he can help the club the most, because that's the important thing," the new manager added.
Carvalhal, whose first task is to prepare for Saturday's trip to 10th-placed Watford, also believes Portugal midfielder Renato Sanches will play a big part in the second half of the season.
The 20-year-old Sanches has struggled since joining on loan from German side Bayern Munich and was offered limited playing time under former boss Clement.
"It is easy to forget because he has played for Benfica and the Portuguese national team that he is still only a kid... He will be involved in the dynamic and when he understands what we want, he will be a completely different player," Carvalhal said.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by John O'Brien)
