A run of just one defeat in their last 10 Premier League matches since a 5-0 drubbing at Bolton in early November has propelled Stoke up to eighth and within 10 points of Pulis' target.
It seems inconceivable the Potteries outfit will be unable to glean those 10 points from the remaining 17 matches and retain their place in the top flight for what would be a fifth consecutive season.
However, until that stage, Pulis cannot rest as he said: "That 40-point barrier is everything, and I mean everything. We have to get Premier League status for next season again.
"It's the thing we desire at this football club, with everything else a sideshow in many respects. Premier League football is so, so important, and we have to make sure we are always focused on that.
"Of course, we enjoy the cup games, we enjoy the challenge, and I feel we've been able to balance things well since we came up into the Premier League. We've done pretty well in the cup competitions.
"But the focus is on those 40 points. We have to get that because it keeps us in the Premier League, and that is the case again this year, to get to 40 points as quick as we can.
"We need just 10 points, and we need to get them as quick as we can, and then push on from there.
"If we can do it in the next seven or eight games, brilliant. We'll be absolutely delighted, and then as I say we can push on.
"But until we do get them I certainly won't be relaxed. When we do, then I'll be doing somersaults."
Despite Stoke's relatively lofty position, Pulis is not even affording himself a cursory glance up the table, with his focus instead on those clubs below him.
"No, not at all," was Pulis' response when asked if he was looking upwards.
"I'm very set in my ways because what people don't realise, what people forget is just how difficult this league is.
"Just look at last weekend's results with Swansea beating Arsenal, Wolves going to Tottenham and getting a result, and ourselves going to Liverpool and getting a result.
"It's the hardest league in the world. You don't get those results anywhere else in the world. You look at the top teams in other countries, they beat the smaller teams all the time.
"But you come to England and you get those kind of results because it is such a competitive league, and everybody is working so hard to ensure they retain Premier League status.
"So we should never take things for granted. We want to be a Premier League club for years and years to come, and to do that you have to stay really focused, and not just us on the pitch, but everybody around us as well."
Stoke face a West Brom side at the Britannia Stadium who have slumped on the back of three consecutive league defeats.
The formbook indicates it will likely be four in a row for the Baggies as they have not won at Stoke for 30 years, losing 13 and drawing five of the 18 matches played.
Pulis, though, is taking nothing for granted, adding: "It does obviously throw itself up, with certain clubs having a say over another club, but I don't know why that is.
"But we'll go into the game with no pretensions at all. We have to be full throttle and give it everything we possibly can, otherwise if we don't then we'll lose."
