United head to Wigan on New Year's Day with a seven-point lead over rivals City, having taken 37 points from a possible 42 since they were beaten by Tottenham at Old Trafford at the end of September.
But Giggs, a veteran of all 12 Premier League championship triumphs, insists it is far too early to think the job is done.
"We were this many points ahead with fewer games to go last season and it wasn't enough," said Giggs. We are only halfway there and there are a lot of tough games to come.
"We are in a great position and are happy where we are, but we know we have to carry on.
"From the manager's experience and the players who have been here a long time, we know Christmas is the time to get down to business.
"If we are there or thereabouts in January and then go on a run of winning 10 or 12 games it is going to give us a great chance.
"There can be no mistakes. But usually when the stakes are high and the concentration is there, good players produce the goods."
Warning against complacency against Wigan, who sit just a point above the drop zone but head into Tuesday's game on the back of a 3-0 win at Aston Villa, he added: "They play with a different system to the ones we are used to and do it very well.
"When you don't turn up against a team in good form you will come unstuck, no matter who you are against."