Barclay left the Warriors for Wales two seasons before they clinched their maiden title.
But the back-row has now skippered Scarlets to Saturday's final against Munster after a stunning semi-final win over Leinster in Dublin.
"I said to our coach today, it reminds me a lot of where Glasgow were one or two years ago," Barclay said.
"All these young guys pushing through who are now playing regularly for Scotland; I can see that happening here."
Barclay, 30, led his 14-man team to victory in Friday's last-four clash as they became the first away side to win a semi-final in the league's history.
He says the Scarlets squad is the strongest he has seen in his five years in Llanelli.
"I've never played in a final, never mind won anything at club level," he told BBC Scotland.
"I left Glasgow and the following year they got to the final. The year after, they won it.
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"I always looked on with a little bit of envy - a lot of my close friends played in that team and they say it was unbelievable."
Barclay says it would be a personal career highlight to win the final and does not think some of his team-mates will be distracted by selection to this summer's British and Irish Lions squad.
"Guys like Jon Davies and Liam Williams, you wouldn't blame them if they had one eye on the Lions tour," he said.
"But, the way they're playing, Jon is probably playing the best rugby I've ever seen him play for Scarlets."
After injury sidelined Greig Laidlaw in the defeat by France, Barclay assumed the Scotland captaincy for the remaining three Six Nations fixtures against Wales, England and Italy.
With Laidlaw's late call-up to the Lions touring party, Barclay retains the leadership of the squad for the June fixtures against Italy, Australia and Fiji - Gregor Townsend's first as head coach.
However, his ongoing involvement with the Scarlets' season finale means the 60-cap player will miss the first fortnight of the pre-tour camp.
"I still wasn't sure if Gregor would come in and completely change things as sometimes happens with a new coach," said Barclay.
"I had a couple of years out of the Scotland squad, I'm always on edge a bit more around selection times; I certainly don't ever expect to be playing.
"That's why I'm not too fussed about the length of seasons, or feeling beat-up or fatigued. I'm just enjoying being involved and playing rugby still.
"Gregor phoned me before to let me know I was going to be captain. He wanted me to focus on playing for the Scarlets for the next few weeks and not fill my head with Scotland stuff.
"It's a bit different to a Six Nations or Autumn Test series, but I wouldn't have it any other way. I've played a long time and not been in a final.
"Part of it is missing out on a bit of preparation, but the other half of that is I'll still be playing competitive rugby two weeks before the first game, whereas a lot of the guys will have had three or four weeks off."
Scotland tackle Italy in Singapore, the Wallabies in Sydney and the Fijians in Suva on consecutive Saturdays next month.
Barclay hopes the squad can continue developing after their most successful Six Nations in 11 years - and he feels this assortment of players is among the most talented of his career.
"If we play a similar brand of rugby, play really exciting rugby, play to our potential, we'll have a successful tour," he said.
"We've got a pretty small pool of players and sometimes it's tricky to expand that without it being to the detriment of the performance.
"It does seem that this is a particularly good group of guys - young guys, guys that are playing the right sort of rugby."
Scotland captain John Barclay sees parallels with his Scarlets side and Glasgow's 2015 Pro12-winning vintage.