The Spanish striker joined for a club record £15.5m from Atletico Madrid in August, 2016, but only scored once.
Borja, 24, almost joined Villarreal on loan in January, but the move fell through.
Meanwhile Swans are monitoring South Korea midfielder Ki Sung-Yueng, who has had minor surgery on a knee injury.
Swans' medical staff visited Ki in Asia and will allow the South Korea captain to recover there before he comes back to Wales after Paul Clement's side have returned from their pre-season trip to America.
The club do not believe Ki's problem is a long-term one, yet they have not revealed a concrete timetable for his recovery.