Godin, 32, has become one of the world's elite defenders since he teamed up with Diego Simeone in the Spanish capital.
That talent, not to mention his cut-price €20 million (£18m/$23.2m) buyout clause, attracted the attention of Manchester United over the summer.
Goal understands, however, that United's enquiry was firmly rebuffed, with the Red Devils told Godin was set to sign a new deal at the Wanda Metropolitano.
And the player himself has now revealed that he had no intention of leaving his adopted home in Madrid, although he is yet to pen an extension.
"I have not renewed," Godin told reporters ahead of Atletico Madrid's UEFA Super Cup clash against rivals Real Madrid.
"I have had offers, although I have decided to stay for personal reasons and I am only thinking about the final.
"But I have not extended my contract.
"I saw that news came out but I do not know where it came from."
Godin has made 350 Atletico appearances since moving from Liga rivals Villarreal in 2010, scoring 23 goals.