Neville has been struggling with injuries in recent years and his contract was set to expire at the end of last term.
But the veteran full-back eventually signed a 12-month deal.
“I turned round during training one morning and said ‘I have three games to go at Manchester United’,” said Neville.
“I had not spoken to the club and I genuinely felt it could be the last three weeks.
“The club didn’t owe me anything and I was more than happy. I was enjoying myself.
“In some ways, my best football came in a period I thought I was just going to enjoy.”
He added: “Because of my injuries, I have thought about the fact I might have to find something else.
“Two years ago I thought it would be my last season. Obviously last year I felt the same. I recognise this one could be as well.
“I am on a one-year contract. If I don’t perform or I feel the club don’t want me anymore I will be gone.
“That is life. In the 19 years I have been here, it has happened to better players.”