The pair were opposing right-backs on Saturday and it was Trippier's Burnley who came out on top in a 1-0 victory over Southampton.
Clyne's form with Saints over the past two years earned the attention of Roy Hodgson and he made his England debut last month in the Euro 2016 qualifying victory over Slovenia.
Trippier has been Burnley's stand-out player so far this season along with striker Danny Ings and he remains hopeful of adding to the caps he won from Under-18s to Under-21s level.
Nathaniel Clyne has flourished since joining the England setup
Seeing a player like Clyne from one of the Premier League's smaller sides given a chance provides added encouragement for the 24-year-old.
Trippier said: "He deserves it. He's been brilliant this year and last year. I used to watch him a lot last season. He's a great right-back and I can learn off Nathaniel because he's played a lot of games in the Premier League.
"Of course it [gives me hope]. I watched him a lot when he was at Palace and now he's stepped up to Southampton and done brilliantly.
"I'm delighted for him but of course everyone wants to play for your country and I'm no different.
"There's no rush. I'll just keep focusing on my performances and see where it takes me."
