The Portuguese coach's representatives are said to have contacted Celtic.
The Scottish Sun claims Carvalhal's representatives have contacted Celtic about the job presently held on an interim basis by Neil Lennon.
But it is unclear what response, if any, that has received from the Parkhead hierarchy.
Carvalhal is not currently among the favourites to be Celtic's next boss.
And a return to Braga, his hometown club and the one he briefly managed 13 years ago, may appeal to the 53-year-old if his quest to return to British football fails.
Braga's existing boss, Abel Ferreira, has been strongly linked with a move to Nantes.
Should Carvalhal return to Braga, he could go head-to-head with his former Sheffield Wednesday and Swansea City assistant coach, Bruno Lage, who has just led Benfica to the Portuguese title.
Should Celtic consider Carvalhal as manager?
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