The 25-year-old has spent his entire career in Spain but reports claim he could be heading to the UK ahead of the 2018-19 campaign.
Iglesias began his professional career with Villarreal before linking up with Celta in 2013, however, has struggled to force his way into the first-team picture.
Celta agreed to loan the striker to Real Zaragoza for the 2017-18 season and he has netted nine times in 23 appearances to catch the eye of Swansea.
The latest reports coming out of Spain suggest that Swansea have been monitoring his progress this term with a view to taking him to the Liberty Stadium.
He will be available for free as his current deal is set to expire at the end of the term, but Swansea will need to convince him to snub an offer from Scottish champions Celtic.