Spanish outlet El Periodico de Aragon suggest that both clubs are hoping to do a deal in the summer.
Iglesias is currently playing in the Spanish Secunda division, where he has 15 goals to his name in 29 league appearances.
At 25, he is still at the ideal age to improve his game and settle in a new league. It is unclear whether he would prefer to join Swansea or Celtic, or stay in Spain.
But it is certain both teams will make a big effort to prize him away from Vigo in the summe