The 26-year-old is expected to attract interest in the transfer market following his impressive performances for Iceland at Euro2016 but he intends to see out his contract with the Welsh club.
"We had a very good last few months as a team because we'd been pretty poor over the first half of the season," Sigurdsson said. "But we got better.
"I've got another couple of years left on my contract and I'm very happy, I'm not running away.
"There hasn't been any talks with Swansea yet because of the Euros but hopefully I'll get a call this week."