Mesa is expected to fly to South Wales this week for talks with the Premier League club confident of agreeing terms. AS Roma were interested in signing the 28-year-old but have yet to formalise a bid.
After time with Huracan and Levante B, Mesa returned to the Canary Islands for a spell with Tenerife B for a season. That was a prelude to a homecoming on his native Gran Canaria in 2011 to join Las Palmas B.
Since then, he has made over 100 appearances for the first team and was a pivotal member of the side which won promotion to the Primera Division in 2014/15.
The playmaker would be the first permanent deal struck by Paul Clement this summer, following the arrival of Chelsea striker Tammy Abraham, on a season-long loan.
Swansea found fine form at the end of the season and won their battle against relegation, at the expense of Hull City. Clement is looking to improve the club’s standing in the new campaign and instil belief into a previously beleaguered squad.