United head to Wigan on New Year's Day 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."