QPR are resigned to losing a number of top stars in the wake of their relegation from the Premier League and Swansea are hoping to lure Granero to the Liberty Stadium.
Swansea boss Michael Laudrup is thought to be an admirer of Granero having worked with the 26-year-old during his time in charge of Getafe.
Granero's agent, Carlo Cutropia, has claimed talks are ongoing between the two clubs and that the Spaniard would be keen on a move to south Wales.
"The two clubs are talking about a transfer, it's true," Cutropia told Tuttomercatoweb.
"Michael Laudrup knows him very well from their time at Getafe, where together they had a great UEFA Cup campaign.
"Swansea are also looking at many Spanish players and play in Europe next year, [so] the destination would be absolutely acceptable to Esteban."
Granero, who joined QPR last summer from Real Madrid, made 27 appearances in all competitions for Rangers last season.