Carvalhal is out of contract at the end of the season but had been in talks to remain at the Liberty Stadium. But their form has collapsed since then.
Britton was signed permanently that summer following contributions towards his wages by fans in a Swansea Supporters Trust initiative labelled "The Battle for Britton".
"So it would make sense to make a quick appointment, but I can't shape that or dictate that, that's a decision for the club".
"I think he was given the job on the [basis] of he could get them promotion out of the Championship [next season] - so they are playing without fear and that's a different prospect".
The former Sheffield Wednesday boss managed to improve results initially with memorable wins over the likes of Arsenal, but Swansea's form has dropped off dramatically. I have done everything I can to put this club in a healthy position.
"I'm not for one minute suggesting Swansea had anything to do with that", Hughes said of the hotel row.
Swansea City midfielder Leon Britton has announced he will retire at the end of the season, with the club seemingly destined for relegation to the Championship.
"The base for me in the future will always be Swansea".
Britton will take Renato Sanches' place on the bench and will play some part, while Rangel is also likely to be a substitute and will come on if circumstances allow.
"Angel will not be in the beginning".
Club skipper Rangel, whose contract is up this summer, has racked up nearly 400 appearances during his time on the Swans' books.