The 28-year-old is out of contract at the Stadium of Light this summer, with reports suggesting that he will leave the Black Cats.
However, the Sweden international has insisted that he is keeping his options open.
"I've never closed the door. It depends on what the conversations provide, what the club want and I want," The Journal quotes him as saying.
"We've had a turbulent two years, but purely socially and in terms of football it has been a good place to be even though it's been up and down. But that does not mean I have signed for them.
"Thinking about leaving if there is a chance to stay would be pretty difficult. But I'm still open. We look at the options available and will pick out the one that feels best."
Larsson joined Sunderland from Birmingham City in 2011.