Sam Allardyce expects to be frustrated in his pursuit of Arsenal defender Mathieu Debuchy, having also given up on a speculative attempt to lure Andre Ayew to Sunderland.
Arsenal full-back Debuchy has been linked with a host of clubs in January, including Aston Villa and Roma, having made just seven appearances in all competitions for the Gunners this term.
The France international has signalled his desire to leave the Emirates Stadium, telling L'Equipe: "I have to go this winter. I cannot stay at Arsenal."
But, with Arsenal still competing on three fronts this term, Allardyce doubts Arsenal manager Arsene Wenger will sanction a sale.
"I'm not sure he really wants to leave Arsenal, or that Arsene Wenger would let him go," the Sunderland boss told a news conference.
Ayew, who only joined Swansea from Marseille in June, has emerged as a surprise target for the Black Cats as Allardyce looks to remould his squad in an attempt to stave off relegation.
The Ghana international has eight goals in 22 Premier League games to his name this season. Jermain Defoe is Sunderland's top scorer with nine in 19 outings, followed by Steven Fletcher with just four.
"Have we given up? Yes," Allardyce said of the Ayew chase.
"I can't see Swansea selling Andre Ayew. I never really thought they would to be honest, and we haven't put a bid in. It was a bit more speculation about whether Swansea would let him go."
Sebastian Coates' loan move to Sporting CP was confirmed on Thursday, making the Uruguayan the sixth player to leave the Stadium of Light this month, and Allardyce expects more to follow.
"It's a balancing act, and if we move people out it helps free up wages," he said. "Jordi Gomez may go, and then there's also Adam Matthews, who might go somewhere to play some football."