United head to Wigan tomorrow having taken 37 points from a possible 42 since they were beaten by Tottenham at Old Trafford at the end of September.
Manchester City and Chelsea performed well over the weekend but there is nothing either of them can do to prevent United securing a record 20th title if Sir Alex Ferguson's men maintain their present form.
But Giggs, a veteran of all 12 Premier League championship triumphs, acknowledges it is far too early to start thinking the job is done.
The Welshman only needs to look back a matter of months, when the Red Devils blew an eight-point lead in the space of four games to lose out to City in the 2011-12 title race, to know nothing can be taken for granted.
"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.
"There is also the FA Cup and the Champions League, so there are other things to consider.
"We are in a great position and are happy where we are, but we know we have to carry on."
However, Giggs does concur with his manager, who has always felt United would be in contention if they reached New Year's Day within striking distance of top spot.
This time, Ferguson can spend his 71st birthday peering down on the rest, with many pundits already declaring it is United's title to lose.
"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," said the 39-year-old.
"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."
It was not the case last season though.
The start of the unravelling process can be traced to a trip to Wigan, a side United had beaten every time they had met up to that point.
Inexplicably, Ferguson's team were caught cold, found themselves unable to cope with Wigan's three-man defensive formation and slipped to a deserved defeat.
It was part of a staggering run from the Latics, which took them clear of relegation trouble when at one point they had seemed certain for the drop.
Their form was so good Giggs was not expecting to find them back in the mire this term.
"I'm surprised that they're down there considering the tough game they gave us last season," he said.
"They play with a different system to the ones we are used to and do it very well.
"We knew they were in a false position going into that game and when you don't turn up against a team in good form you will come unstuck, no matter who you are against.
"It was tough, especially when you consider our record there and it undoubtedly contributed to us losing the title."
Ferguson is expected to make a number of changes given the draining conditions his players encountered at Old Trafford during Saturday's win over West Brom.
Michael Carrick looked particularly tired, whilst Robin van Persie's 17th goal of the season should ensure his recall at a time of year when freak results are almost commonplace.
"When you have got four games in nine days you are going to get different results and things can change quite quickly," said Ferguson.
"The most important thing is not to panic and look after your own results and performances."