It is understood that the Swans have a pre-contract agreement in place with the midfielder, meaning he will be free to make a move to the Liberty Stadium at the end of the season.
Michael Laudrup is, however, exploring the possibility of paying a fee and bringing Canas on board during the winter window.
Betis will not allow Canas to leave on the cheap, though, and have informed Swansea that they will either have to pay the going rate or wait until the summer to get their man.
"It has been decided, unless Swansea say something different, that Canas stays here until 30 June," said Betis boss Pepe Mel.
Canas was left out of Betis' squad for a cup clash with Las Palmas on Thursday, but Mel insists that decision was based on a slight knee problem rather than any outstanding issues regarding his future.
He added: "He is a committed played. He gives everything and stood out as he always does.
"We left him out for the cup game as a precaution but he will train as normal after that."