The 27-year-old's current agreement is said to expire at the end of the 2012/13 campaign.
The Dutch full-back had previously claimed that he did not expect to be at the Liberty Stadium next season.
He has, however, now revealed that he is set to sit down with the Swans and attempt to thrash out fresh terms.
Having made 21 appearances for the League Cup winners this term, Tiendalli said in The Sun: "Me and the club are going to talk about the future and we will see where it ends.
"We're going to talk this week. It's not just about the last couple of weeks, it's about all the games.
"I have a feeling I did my job well and we will see what happens.
"Of course I want to stay. I like Swansea."
Meanwhile, as Tiendalli plans for an extended stay in South Wales, Mark Gower has confirmed that he is heading out of Swansea.
The 34-year-old midfielder has agreed to terminate his contract a month early, allowing him to search for a new club.
He said in The Sun: "I'm sad to be leaving, but it is in the best interests of both myself and the club.
"It could not have gone much better for me. The club has only gone in one direction and that's up.
"If someone had said to me the day I signed here that we'd get into the Premier League, win the League Cup and get into Europe then I'd need some convincing.
"But that's what we have done, and everyone here has played their part and should feel so proud with everything that has been achieved."