The midfielder has been virtually ever-present in the Verdiblancos side this season, playing 26 League games so far for Pepe Mel's men.
But 20 Minutos has claimed that the 25-year-old, whose contract in Andalusia runs out in June, has agreed to join the Premier League side for free next term.
Canas would be another player from La Liga to sign for the Welsh team, joining the likes of Michu, Chico Flores and Pablo Hernandez.
Such a deal would imply that on-loan Villarreal midfielder Jonathan De Guzman may not stay at Swansea after this season, with Liverpool reportedly interested in the Netherlands international.
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- Chico Flores