New Sevilla boss Jorge Sampaoli sees no place in his side for the 31-year-old and Sevilla's sporting director Monchi confirmed a deal was almost done.
"It has come a long way with Swansea to reach an agreement, we expect to hear in the coming days," he announced on Sevilla's club website.
Swansea have been desperately searching for a striker with Euro 2016 hero Eder, Bafetimbi Gomis and Alberto Paloschi all leaving the club.