According to the 'Daily Mail', Swansea have made a concrete offer for the striker who is valued at £6 million by his current club.
The target man has 145 goals in 455 appearances in a career that has seen him play for Athletic Bilbao, Juventus and Sevilla.
The 31-year-old was also in Spain's squads for their World Cup win in 2010 and their Euro 2012 triumph.
It appears that Swansea manager Francesco Guidolin's main priority is to bring in a 'number nine', with the Swans also being linked with Leicester's Leonardo Ulloa and Stoke City's Peter Crouch.