The Norwegian will see his current contract with the Birmingham club expire next summer, and he is yet to pen fresh terms.
He is prepared to keep the door open to the Villans, having become a firm fans' favourite during his three years in England.
Carew is refusing to rule out the prospect of taking on a new challenge elsewhere, though, as at 31 years of age his career is starting to edge towards a close.
"I am in a very comfortable position," he told fvn.no.
"The spell at Villa has been fantastic. I will now see what opportunities and challenges turn up.
"I have enjoyed myself in England but it's possible that something interesting will come up."
Over the course of a distinguished career, Carew has already turned out in Norway, Spain, Italy, Turkey and France.