The midfielder was heavily linked with a move to the Hammers in the summer but a deal collapsed at the 11th hour.
West Ham's owners and Sporting Lisbon then fell out as part of a public spat, which has left relations between the two clubs in tatters.
But, according to Record, Carvalho is desperate to leave Sporting Lisbon when the transfer window opens.
The Portugal international is said to be unhappy where he is and he wants a fresh challenge.
That news will be of interest to West Ham, but it could also intrigue Arsenal – who are long-term admirers of Carvalho.