Chairman Huw Jenkins is determined to retain the services of the Welsh side's goalkeeper, centre-back and left-back as they look to cement their status in the Premier League
Both Holland international Vorm and Swans captain Williams have been linked with former boss Brendan Rodgers at Liverpool, but chairman Huw Jenkins wants to retain the stars.
"We are working on quite a few things," Jenkins told reporters.
"We are looking to make sure we have got a few of our experienced players on extended deals.
"That's something we are looking to do at the moment and we're optimistic that we'll be able to get things sorted with a number of players."
Vorm and Williams have two years remaining on their current deals whilst Taylor, who is sidelined with a broken ankle and is unlikely to play again this season, has three years left.
The trio are seen as indispensible to Michael Laudrup's side, and Jenkins insisted that Taylor's injury will not affect the deal, which the former Stockport County man has agreed to.
"Neil's injury does not impact on the contract situation," Jenkins continued.
"The discussions with Neil were more or less concluded before the injury and nothing has changed.
"Hopefully things will be finalised soon."
The player himself has confirmed that he will sign the deal, which will see him extend his four-year stay at the Liberty Stadium.
"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."