The Magpies are up against stiff competition with Liverpool and Manchester City also set for a summer move for the former Arsenal frontman.
Reports from Spain have suggested that Newcastle are leading the race to sign the 24-year-old Atletico Madrid striker, as Reyes has suggested he wants to return to England.
Vice-president (player recruitment) Tony Jimenez is understood to have identified the Spain international as a potential target, although other clubs are said to be monitoring his situation.