The left back who joined from Wrexham last summer has been strongly linked with a move away to the North East in the past few weeks, with Everton also credited with an interest.
It was revealed that Taylor could speak with a club if they offered just £1m, due to a clause in the Welshman's contract, but this does not mean that Swansea have to accept £1m for a player who they have brought into the spotlight.
One of yesterday's newspapers claimed that Taylor was ready to sue the Swans over their stance to keep him at the club, although how much credence can be given to the article is questionable, as it also went on to state that the board were holding out for £10m for the player.
Huw Jenkins simply says that the bid has been rejected because the club sees Taylor as an important part of the squad.
"We recognise Neil as a young, talented Welsh player that has an important role to play at this club," Jenkins told the official site.
"We brought him here from Wrexham and have helped nurture his development. He adjusted very well to the Championship last season and we look forward to seeing him play a big role as we enter the Premier League.
"That is why we have rejected Newcastle's bid. I spoke to Neil's agent today and he understands the situation.
"We have a big challenge ahead in the Premier League, but together we can maintain the progress made by this club over the last few years."