But Godin, who won a LaLiga title, a Copa del Rey and a pair of Europa League trophies during his time at Atletico, has no intention of moving on.
"The truth is that I was surprised by this news. Since I came to this club I have always felt very comfortable," Godin said.
"Both the club and the fans welcomed me very well and from day one I felt at home.
"It never occurred to me to leave Inter. I feel totally identified with the project. The human group is spectacular."
Godin said his ambition is still to win major honours with Inter and he will honour the length of his deal and beyond if the club wants to keep him.
"My intention is to fulfil my contract and enjoy this wonderful stage in Italy and Inter, who trusted me," he added.
"I took responsibility and came with the intention of helping to get titles again. Here I am happy and I know that the feeling of the club is the same, which fills me with pride.
"I do not understand why some media insist that I am looking for a way out, when they know that this is a lie.
"I have never spoken to anyone on this subject, because it is simply not true. I'm going to stay here, and try to help the team in whatever they need.
"And if they continue to be happy with me, my time at Inter will be extended as long as they want."
Inter were back in action after the three-month coronavirus-enforced suspension with a 1-1 draw at Napoli in the Coppa Italia last Saturday, a result that saw them miss out on the final in a 2-1 aggregate defeat.
They return to Serie A action with a home fixture against Sampdoria on Sunday, with Inter third in the table and nine points adrift of leaders Juventus.