The champions and current Aviva Premiership table-toppers head to Kingsholm hoping to claim a 14th win in 17 league games this season.
But with Saracens, Leicester and Sale having already tasted defeat at eighth-placed Gloucester this season, Saints are wary.
And with six games of the regular season remaining, King is keen to ensure there is no slip up this weekend.
“Every game is tough and you have to work incredibly hard to get the points,” he said.
“We’re not looking too far ahead. We’re looking at Gloucester away on Saturday and it’s another opportunity to get some points on the board against a team who feel their form merits a higher league position.
“It’s going to be a huge challenge down there at Kingsholm, which is one of the great rugby venues in English rugby, and the boys are really looking forward to it.
Saints were stung by a dramatic defeat on their last visit to Kingsholm, as a last-gasp Billy Twelvetrees penalty gave the Cherry and Whites a 26-24 win in September, 2013.
Jamie Elliott scored one of the tries of the season in that match, but the stunning effort proved to be in vain.
And King said: “It was a good game, a few good tries for either team and it was settled in the last minute by a penalty, but that’s the season.
“You do get games like that, which ebb and flow.
“Some things go for you, some go against you but it’s a long time ago now and we’ve got a huge amount to play for and we’re really looking forward to it.”