Gomez has started just three times since Allardyce was appointed as Sunderland boss, with the Spaniard not even included on the bench for the last five games.
Sunderland have already eased the strain on their wage bill this month by offloading Danny Graham, Costel Pantilimon, Will Buckley and Liam Bridcutt.
But with another 18 months remaining on Gomez’s contract at the Stadium of Light, Allardyce admits that it would suit all parties if the ex-Wigan man moves on over the next nine days.
Allardyce said: “I think with Jordi Gomez not playing as often as he’d like, then it’s probably a yes over whether he could go before the deadline.
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“There’d be no problem with us if Jordi wanted to find more regular first-team football.
“We both agree in that department that it would be the right thing to do for both of us.”
Gomez might not be the only further departure either, with Valentin Roberge and Charis Mavrias also still on the club’s books, albeit the latter featured in the FA Cup third round defeat at Arsenal earlier this month.
“It depends on whether anyone comes in and we can strike a deal,” said Allardyce on the possibility of more players leaving.
“If the deal is right for the football club, then I would suggest to the owner that it’s right to do this deal.
“But if not, I’m happy with the squad we’ve got, if we can bring in one or two more players.”
Sunderland have needed to offload players this month to free up funds that can be reinvested in new signings.
Despite already bringing in Jan Kirchhoff and Dame N’Doye this month, Allardyce remains eager to add a defender, attacker and third-choice goalkeeper before the window shuts on Monday-week.
Sunderland remain in negotiations for Swansea forward Andre Ayew, albeit speculation persists in Italy that the Black Cats are in the running for Fiorentina frontman Khouma Babacar.