The Gunners are looking to strengthen at the back in January and Wales international Taylor has been linked with a move to the club.
Taylor signed a new four-year contract with Swansea in the summer.
“I’m flattered by the interest from Arsenal,” said the 22-year-old in the Daily Star.
“I’m enjoying my football at Swansea but it’s a great thing to hear.”
“I’ve had a few texts off people telling me, but I just get on with my football,” Taylor told BBC Sport. “I’m enjoying my football here and I think it’s going great.
“Every player should be getting watched at the moment because we’re a young outfit and we’re doing really well.
“We play some exciting stuff and I think a lot of people are talking about us which we want to just keep doing.
“We’re hard working bunch and as long as we stay together and keep going, we’ll be successful as a team.”
