Brazilian playmaker Lucas Moura has extended his contract with French champions Paris Saint-Germain until 2019.
Burnley's new sporting director Frank McParland hopes to be able to start next season alongside Sean Dyche.
The goalkeeper has been named the player of the season at the Liberty Stadium as Brendan Rodgers' side have exceeded expectations in their debut Premier League campaign.
Vorm has consequently been linked with a transfer to other clubs and Arsenal are rumoured to want the Dutch international as back-up to Wojciech Szczesny.
But ahead of Sunday's season finale against Liverpool, Vorm, a £1.5million summer 2011 signing from FC Utrecht, said: "I think I will stay at Swansea. I like it here.
"I am number one and we play the league's best football. There are not many better places I could go. Why should I go and sit on the bench somewhere?"
He added: "It's been a very special season, especially as it's my first at the club."