The former Wales international celebrated his 40th birthday on Friday and is out of contract in the summer.
Given his performance against Bayer Leverkusen in midweek, speculation has already turned to whether Giggs will be offered a contract extension, but Moyes does not feel it is the right time to discuss such matters.
"When you get to this age it is always a late decision and you wait until the end of the season," said the United manger.
"It is based on how you feel, how you have done over the year and what your body is telling you."
But there is no doubt that when Giggs eventually decides it is time to end his career, it will be remembered as one of the finest there has ever been.
Giggs has spent his whole career at Old Trafford and has made 953 appearances for the Red Devils since making his debut in 1991.
"He's undoubtedly at the top because of his longevity and the time that he has played for just one club, the amount of games he has played in Europe and in the Premier League," said Moyes.
"Every season, you can look at Ryan Giggs moments. To be playing so well at his age is terrific and a great example to young players about how you should dedicate yourself throughout your career.
"It also tells players who get into their early to mid-30s and think things are coming to an end that if they really look after themselves and train well, they can go on for a lot longer."
United's players all wore Giggs face masks to greet the arrival of the 40th birthday boy on Friday.
Giggs was also presented with a watch and the players' changing room at the Aon Training Complex was plastered with pictures of the veteran, who had threatened to stay in bed to avoid any potential pranks to mark his big day.
"Everyone had a Ryan Giggs mask on," Moyes told MUTV.
"The dressing room was full of pictures of him. He looked as though he was in a boy band when he was much younger.
"They also got him a coach's watch - I think they are trying to push him out of the door - but he took it well."
Arsenal boss Arsene Wenger said of his long-time opponent: "If I'm 20 per cent above the normal level at a young age and I drop 10 per cent, I'm still 10 per cent above everybody else. That's what happened to Ryan Giggs.
"What he has done is absolutely exceptional. I always thought that Ryan Giggs did not always get the reward or the recognition for his quality and his huge career because he did not play in the World Cup and the European Championship.
"You look at his club career - it's absolutely unbelievable. The quality of his performances show a masterclass at 40. What is very remarkable in his case is that he has turned from being an individual player into being a good passer and a collective player.
"That is a very difficult transformation and that shows you that he not only had individual quality but the intelligence and understanding of the game as well.
"People like Thierry Henry [also] had exceptional qualities," added Wenger. "They would run 100 metres in 11 seconds when everybody else did it in 12.5 or 13. So if today they are running it in 12, they are still quicker.
"They start from a huge potential and that's why at that age they can still survive, because they have the football intelligence. They had exceptional physical qualities at the start."
Stoke boss Mark Hughes played with Giggs for both United and Wales in the 1990s, and was also quick to talk up his achievements.
He said: "He is the legend of the Premier League. I remember him breaking through into the first-team squad and Ryan was the shining light in that group of players. No one will repeat what he has achieved.
"It was always evident that he was an exceptional talent. Nobody in training could get anywhere near him and we nicknamed him 'Sidewinder'. I'm amazed that he's adapted to the modern game so well in his later years."
Another former team-mate, Hull manager Steve Bruce, added: "There'll never be anybody else who can play at that level from the age of 17 to the age of 40. It's quite unbelievable. Even when you see him last week, he's still as fit as a flea and still has the hunger and desire to be a player.
"He still enjoys football so much. It's quite remarkable what he's achieved and he's the only one I've ever known who was a certainty. We've all seen youngsters and said 'he's a hell of a player' but he was a certainty when he was 14 or 15.
"We used to say when he ran around us when he was younger that it was so effortless, and even now he never seems to be exerting. He's blessed with a natural ability to move and run and is a wonderful athlete."