The Anfield club are going through a period of transition with Roy Hodgson replacing Rafael Benitez after they finished seventh in the table last time around.
However Hodgson has already persuaded England midfielder Joe Cole to sign up after his contract ended at Chelsea and Giggs believes their rivals deserve respect.
"Liverpool have a new manager and difficult to say what they are going to do, " said Manchester United's record appearance holder.
"Two years ago they were close to winning the Premiership and you can never write them off. It just depends on how it goes.
"It is dangerous to write off a team with Liverpool's history. They have won the same amount of leagues as us. You cannot just dismiss that. They are a huge club and a massive team."
United are aiming to wrest the crown back from Chelsea and Giggs feels six or seven clubs will be in the mix.
Those include Manchester City, who ended last season just outside a Champions League place in fifth position.
Giggs enjoys the derby matches and said: "The rivalry has always been there but it has been turned up a notch purely because of how much money they have got.
"I felt that last season with the first game. The build up to it was huge. The world was watching.
"They were watching the biggest team in the world, which is us and the richest team in the world, which is them. So it is great for the city to have that sort of interest."
At 36, Giggs shows no signs of slowing down and is training hard during their five-match summer tour from Canada to the United States and then to Mexico.
"I enjoy it more than ever. When I stop enjoying it, I will stop. I still have the hunger, the desire, "he told ESPN.
"I still want to train every day, I still want to improve. So when those things stop happening I will finish.
"I started my first pre-season 20 years ago. It was running until you collapsed. You did not see a football for the first two weeks.
"Now it is a lot more detailed, a lot more science. We have football days and days in the gym. It is a lot more technical."