The Uruguayan international had been linked with a move to Manchester United before the English transfer window closed on August 9th.
“I received offers, but decided to stay for personal reasons,” the 32-year-old Godin told Movistar+.
“I have not yet extended (my contract). I've seen a lot of things in the press, but now, what's important is to wait and concentrate on the (UEFA Super Cup) final.”
Europa League winners Atletico take on city rivals and Champions League holders Real Madrid in the Super Cup in Tallinn on Wednesday before the start of the La Liga season this weekend.
Godin has played 350 matches for Atletico since joining from Villarreal eight years ago, winning the Spanish league title in 2014, the Europa League in 2012 and earlier this year, and the 2013 Copa del Rey.
The capital-city club has a policy of “only extending the contracts of players over the age of 30 on an annual basis”, according to Spanish sports daily AS.