Madrid-born Borja has represented Spain at various youth levels
Swansea chairman Trevor Birch says Spanish striker Borja is likely to remain with the Championship club.
The 26-year-old made his first competitive Swans appearance since 2017 in the season opener against Hull.
The Swans had made no secret of their desire to offload the player but with Oli McBurnie leaving for Sheffield United, Borja could be staying.
"The Oli deal has given us flexibility so it remains to be seen whether Borja will stay with us," Birch said.
"The likelihood is he will now and hopefully he makes a good start and we'll see what happens."
Borja joined Swansea in a then record £15.5m move from Atletico Madrid in August 2016
But he has made just 20 Swans appearances, spending the last two seasons on loan at Malaga and Alaves respectively.
Birch said the decision to sell McBurnie to Premier League Sheffield United for £20m had been a difficult one but one they could not turn down
The ex-Chelsea and Leeds United chief executive said the final decision to sell the Scotland international had been his and not the club's American owners,
Trevor Birch was appointed Swansea City chairman in March 2018 following the resignation of Huw Jenkins
"Ultimately it's my decision. I'm the chairman so I'm not abrogating any responsibility for that, I'll take it on the chin," Birch told BBC Radio Wales Sport.
"When you get an offer of that magnitude, the situation we're in, you can't turn it down.
"Imagine turning it down and he breaks his leg and that deal's off and suddenly we have a financial crunch that we knew was coming and then you're in a Bury/Bolton situation.
"We can't afford to let that happen, not under my watch anyhow.
"We didn't intend to do it just prior to the first game but that's just the way the deal developed.
"Sometimes you can't legislate for the timing of these things.
"I'd probably been derelict in doing my duty, because first and foremost you have to protect the financial future of the club."
Swansea's new head coach Steve Cooper has brought in four new players - defender Jake Bidwell and winger Kristoffer Peterson on permanent deals with goalkeeper Freddie Woodman and defender Ben Wilmot joining on loan.
The summer transfer window closes on Thursday and Birch said the Swans are hoping to add to their squad.
"We're still looking and still hopeful of at least one more coming through the door," Birch added.
"I'd say I'm confident that we'll get at least one body through the door."
