The striker has managed nine Premier League goals while on loan at Middlesbrough from Valencia and has attracted attention from the Turkish side
Galatasaray have held talks with Alvaro Negredo according to the Turkish Super Lig club's sporting director Cenk Ergun.
Negredo has spent this season on loan at Middlesbrough from Valencia but the former Sevilla and Manchester City striker's nine goals could not help them avoid relegation from the Premier League.
The 31-year-old, who won the last of his 21 Spain caps in November 2013, appears unlikely to have a future at Valencia and Espanyol were linked to his services by SuperDeporte last month.