The burly Belgian has spent this season with West Brom, turning in a number of impressive displays to help the Baggies into a solid midtable position.
Despite the teenager having netted 13 goals, Chelsea are believed to be keen to send him out again next term to gain more experience.
It was expected that Lukaku would remain at The Hawthorns, but with the World Cup just around the corner the ex-Anderlecht man is keen to build his profile by playing European football.
Swansea are hopeful that they can take advantage of this, with their spot in the Europa League already guaranteed thanks to Capital One Cup success in February.
Michael Laudrup has already stated his desire to bulk out his squad for what could be a difficult season, and he is thought to be a big admirer of the 19-year-old.
The Swans have relied heavily on Michu for goals this term, with the Spaniard often having to play as an out-and-out striker, despite being a midfielder by trade.
Lukaku would offer the Liberty Stadium side an orthodox attacking threat, combining raw power with the level of technique needed for Swansea’s style of play.
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