The Magpies currently lie fifth, level on points with fourth-placed Tottenham with five games to go, and well in contention for a Champions League berth.
Although both Spurs and Manchester City have made their debut in the competition in recent years by breaking into the top four, it would be the biggest surprise yet if the Tyneside outfit - only promoted back to the English top flight just under two years ago - managed to return to Europe's top table.
They last featured in the Champions League when they were eliminated in the qualifying rounds in 2003 and Pulis, whose team play at Newcastle on Saturday, would be delighted to see them rubbing shoulders with the continent's elite once again.
The likes of Senegalese frontman Papiss Cisse and French midfielder Yohan Cabaye - previously relative unknowns - have emerged as stars this season after being recruited by the Magpies, helping the club exceed all expectation by challenging for a place in the top four, and Pulis has been impressed.
"I think it would be lovely for the Premier League to have someone new and fresh getting in there - although I'm sure the rest of the teams up there will have something to say about that as well," Pulis said.
"Alan (Pardew, Newcastle manager) has done a fantastic job but this is the business end of the season now when they have to push forward and push on.
"As with the top two teams (City and league leaders Manchester United), who have got the bit between their teeth - it is who gets their noses over the line first.
"It is great for us as a football nation if you get a team outside what is supposed to be the top six group getting into it and working hard to try to stay there."
Pulis is also determined to continue driving the club forward.
The Potters have made great strides over the last few years under Pulis' guidance, winning promotion to the Barclays Premier League in 2008 and achieving comfortable mid-table finishes in every subsequent season.
Having passed the 40-point mark during the Easter period they appear set for the same again this term, despite the fact they have faced their most demanding schedule yet due chiefly to their participation in the Europa League, which they gained entry to by reaching last year's FA Cup final.
Already with an eye on how he might strengthen his squad over the summer, Pulis has used a rare break in Stoke's fixture list - their last match was the 1-1 draw at Aston Villa on April 9 - to go on a scouting mission to Spain and he is committed to keeping the Staffordshire outfit on an upward trend.
"Every member of the staff went away watching games," Pulis said.
"It was a weekend off, so it was an opportunity to get out and follow up on some leads that we have been given during the season.
"We want to keep moving the football club on. It is very important that you freshen it up and that is what we will try to do if we can."
Stoke are currently 14th in the table, but only a point away from ninth and have their sights set on sealing a top-10 Premier League finish for the first time.
They have five games remaining, with the next being Saturday's at Newcastle, whose ability to spot talent has served them particularly well in recent times.
Meanwhile, Pulis has confirmed Stoke are looking to reach agreement with defender Robert Huth over a new deal.
Huth, who is out of contract at the end of next season, has been linked with a move back to his native Germany this summer but Pulis is hopeful he can retain the 27-year-old's services.
"Huthy has a year left, so there is no immediate rush with him," Pulis said.
"But the club is keen to get something done and so is Robert. So fingers crossed something can be ironed out."