Carvalhal has been out of work since leaving Celta Vigo in June, having kept the club in La Liga courtesy of a dramatic final-day win over Barcelona.
Prior to his stint in Spain, Carvalhal led Rio Ave to a club-record tally of 55 points in Portugal's Primeira Liga in 2019-20, before moving to Braga and winning the Taca de Portugal the following season.
The Portuguese coach is no stranger to the Middle East, having managed UAE Pro League outfit Al Wahda in 2022, and he would not necessarily be against a move to Saudi Arabia.
Saudi Arabian clubs have spent heavily in the transfer market this year, acquiring the likes of Karim Benzema and Neymar after the country's Public Investment Fund took control of four of the league's biggest clubs.
Though many have expressed concern about the financial power of Saudi clubs and the potential for the league to act as a "sportswashing" vehicle for the state, Carvalhal would be open to a move if presented with an attractive project.
"We never know. We never know. I have said that if the project is structured, let's see," Carvalhal told Stats Perform at the Thinking Football Summit when asked if he would manage in the league.
"It has not been a long time. If the project is to buy good players, with good coaches and also to develop youth football, if there are these kinds of projects in the future, I believe they can do something important.
"I remember China six years ago or seven years ago, they bet with very good coaches, very good players and after one moment they decided, 'no, we don't want this anymore, we are spending too much money', and they finished.
"It's over to everybody [in Saudi Arabia], let's see if this is consistent, if it will be here for 15 or 20 years.
"It is very welcome what they are doing – if it's something circumstantial. It's something that we don't know [yet]. "
Carvalhal's Celta side was built largely around the talents of Veiga, who scored twice as they upset Barcelona to clinch survival back in June.
Veiga was linked with Serie A champions Napoli before opting to join Al-Ahli, who also signed Riyad Mahrez, Roberto Firmino, Edouard Mendy, Allan Saint-Maximin and Franck Kessie in the recent window.
Carvalhal is proud to have played a role in Veiga's development, highlighting the way his move brought much-needed funds to Celta.
"Gabri Veiga for Celta Vigo in the B team was like a striker, then we decided to put him in the second midfielder [role] because the way that he plays there, he can score goals and give assists," he said.
"It was a big challenge for him because he started as a striker and after with us, we played with two midfielders, and he was one of the midfielders.
"He has improved to another level in this kind of position, with the goals and breaking lines.
"Of course, when he finished the season and we saw that big clubs wanted him, he moved to Saudi Arabia as an option.
"Big money came into the club, of course. We are very proud and very satisfied about everything."
Celta have four points from five matches under Carvalhal's successor Rafael Benitez, who has become the first coach in the club's history to lose his first three home league games at the helm.