Gomez impressed for the Swans and it is thought that Boro are considering an offer, funded by parachute payments from Premier League relegation and probable player sales.
The 24-year-old, who is believed to be valued at €2million (£1.7million) has stated that he would prefer to stay in Spain but, with La Liga interest limited, he would accept a return to England.
"My dream is to play in the Primera division, but nobody has done anything," Gomez told Spanish media.
"The normal solution would be a move to England and I am mentally prepared for this.
"During the season, many clubs have sent their scouts and I believe the reports are positive.
"But the definitive decision rests with Espanyol."