Giggs, 33, is in talks with chief executive David Gill to extend his Old Trafford career into a 17th year.
He said: "We have had a brief chat, so hopefully it will get sorted sooner rather than later.
Giggs, who has won nine league titles with United and is closing in on Sir Bobby Charlton's record of 754 club games, has a year left on his current deal.
He added: "We trust each other, which comes from 15 or 16 years in the first team. I don't think I need to play well in specific games otherwise I won't be offered a contract. Generally speaking, if I am doing well, everything else will take care of itself.
"It is not something I worry myself about. You could easily get caught up in 'I have only got a year left so I need to play well' and put that added extra pressure on yourself.
"But the pressure playing for United in itself is enough you don't want to put added pressure on.
"I just try to enjoy it because I feel the more I enjoy my game the better I play.
"That has been the case over the last few years because I am coming to the end of my career."