Carvalhal, 52, has managed Sheffield Wednesday and Swansea - along with Turkish outfit Besiktas - in recent years, though departed the Welsh side after their relegation last season.
Having taken a break from football due to a "family problem", Carvalhal is ready to return to management, and spoke to 'Sky Sports'.
He remarked: "When I finished my contract with Swansea, in that moment I had some opportunities to come back to England, but was very sad to reject because I can't because of the situation with my father.
"So situations that two years before maybe I'd come to England swimming to accept those situations [offers] but I must refuse first of all because I must do that.
"But during this period, especially this month when I'm back to the market, it's unbelievable. Different countries, different clubs in different leagues. But my preference is to try and come back to England, which is why I refused all the situations so far."