Mesa is in Spain ahead of a potential medical as the clubs finalize the details, following discussions over the 28-year-old.
He signed for the Swans from Las Palmas for £11m last summer but Sky Sports News understands Mesa is frustrated with his first-team involvement, having made only 11 top-flight appearances for the Premier League's bottom side.
Allowing the 28-year-old to leave the Liberty City stadium on loan would reduce Swansea's wage bill and could free up funds for the club as they continue in their hunt for a striker.
Carlos Carvalhal has already seen his side have a £14m bid rejected by West Ham for Andre Ayew, with the Hammers believed to be holding out for the £20m they paid Swansea for the player in 2016.
Swansea, who sit bottom of the Premier League three points adrift of safety, travel to League Two side Notts County in the fourth round of the FA Cup on Saturday.


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