Sources claim discussions to that affect have been held between the clubs.
The Brazilian top flight does not start until March, which could – in theory – clear the way for such a deal.
But any agreement for Paqueta to stay in London until the final game of the season in May could depend on how far adrift West Ham are from safety.
They are currently six points adrift of Nottingham Forest, who occupy 17th place.
Paqueta missed last weekend’s FA Cup third-round win over Queens Park Rangers, which sparked claims from insiders that he did not make himself available because he wants to leave.
However, club sources insist Paqueta’s absence was down to a minor injury.
It now remains to be seen whether Paqueta is selected to play against Tottenham in the Premier League on Saturday.
