The full-back was recently ruled out for the remainder of the Premier League season with a serious ankle injury.
However, the Welsh international has confirmed that the club are still keen to secure his services.
"We've been talking about a new contract for a few months now," said Taylor. "We were very close before the injury happened. But in fairness to the club they have already said they will honour the new deal despite the fact that I won't play again this season.
"The way they have handled it speaks volumes about the club and the board."
The 23-year-old joined the Swans from Wrexham in 2010.