The midfielder, who celebrated his 40th birthday on Friday, has taken on a coaching role under Moyes, but his future as a player beyond this season remains unclear.
And Moyes believes the player's age means any decision over a potential new deal should not be made on a whim.
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"When you get to his age, any decision about carrying on is left until the end of the season," the Scot told reporters. "Don't forget, he's on the coaching staff anyway, but if he feels he wants to continue next season I'll be more than happy with that.
"Ryan is undoubtedly at the top of any list of Premier League legends, for all sorts of reasons.
"Because of his longevity, playing his entire career at a club like Manchester United, the amount of games he has played in Europe and the Premier League and the fact that he has provided so many outstanding memories every single season.
"It is terrific to be doing it at his age, and it is an example to young players everywhere to see how far you can go with the right dedication.
"It is also an example to players in their mid-30s, who may be wondering whether they are coming to the end of the road, to see that if you keep training well and looking after yourself, you can carry on longer."
Moyes also revealed the squad had bought Giggs a number of gifts to mark the occasion.
"There were a few surprises for him in the dressing room to mark his birthday," he said. "A coach's watch was one, so maybe they are trying to send him a message.
"I think he was beginning to think they were pushing him out of the dressing room.
"They're very good. He's respected by everyone in the dressing-room because of what he's done and what he's achieved in football."
Manchester United take on Tottenham in the Premier League at White Hart Lane on Sunday.