The Uruguay defender was rumoured to be a transfer target for Manchester United on deadline day, but a move failed to materialise.
Speaking ahead of Atletico's Super Cup clash against rivals Real Madrid, however, the 32-year-old poured cold water on the speculation before explaining his reasoning for staying at the Wanda Metropolitano.
"I have not renewed," Godin told The Mirror. "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 was also linked with a move to Italian Serie A champions Juventus earlier in the summer.