Manchester United manager Louis van Gaal has refused to rule out the possibility of signing goalkeeper Victor Valdes.
Manchester City boss Manuel Pellegrini says he is confident that England goalkeeper Joe Hart will sign a new contract.
The 20-year-old Wales international's previous deal had been due to run until 2016..
He told the club's official website: "I'm very happy to have signed the new contract.
"It wasn't a difficult decision and it's always great to sign a new deal and commit my future to the club.
"This is a great place to learn and improve and it's nice to be rewarded for all the effort I've put in.
"I feel as though I'm getting better all the time and this is a good place to play football, especially with the style of play we have at the club.
"I think it's the right place to be at in terms of my career, and if I'm playing regularly and I'm happy then that's the main thing and all I can ask for."
Davies has become one of Swansea's most consistent performers having been thrown into the first team when Neil Taylor broke his ankle in September 2012.
At the time Davies was earning just £400 a month, but the Welsh cub quickly offered him a new deal last November and he went on to make 44 appearances that season as Swansea won the Capital One Cup and finished ninth in the Barclays Premier League.