The quartet - Daniel Bigham, Charlie Tanfield, Jacob Tipper, and Jonathan Wale - finished fourth in Manchester, continuing the remarkable story which started with the British national title in January and continued with seventh place in the opening round of the World Cup in Poland last weekend.
Breaking into the Britain squad would not be easy. Ed Clancy, Steven Burke, Kian Emadi and Oliver Wood stormed to gold in Manchester with a time of three minutes 55.847 seconds, some two and a half seconds faster than KGF.
Britain have won gold in the men's team pursuit at every Olympics since Beijing in 2008, with Clancy part of all three squads and Burke riding in 2012 and 2016.
There is a considerable depth of talent, but Britain's coaches are keen to see for themselves what the youngsters - and their unorthodox tactics, featuring lead turns of up to five laps - have to offer.
"For sure we're going to be looking at the KGF guys over the coming weeks and months," said Great Britain head coach Iain Dyer.
"We've been looking at them for a long time, and there has been a dialogue with us.
"We had meetings with them in Poland and here again, talking about performance issues and selection matters.
"We want to take a closer look at Dan and Charlie in the next month or two and bring them in to do some training."
Dyer stressed that British Cycling has already done its bit to support the amateur outfit, who are coached by Mehdi Kordi, a physiologist who works for British Cycling.
"It's perhaps easy to imagine from the outside that we don't talk to these people, that we don't know who they are, but of course we know them pretty well," he said. "They got to the line with three of our coaches."
KGF's World Cup season may already be over after two rounds as they do not have enough in the kitty to travel to Canada or Chile, though they are hoping to raise enough to race in the final meeting in Minsk in January.
It may not matter if they can spend the time with British Cycling instead.
"It's great that they're coming in, providing a little bit of pressure to show the guys there's always someone chasing," said Great Britain performance director Stephen Park.
"They've been smart about what they're doing and making people think a bit. From that perspective, it's great."
Clancy got his first real look at KGF this weekend as he raced on the track for the first time since Rio.
"You look at those four guys and think, fair play," the 32-year-old said. "I've never met some of the guys. I know one has a degree in aeronautical engineering (Bigham) and I've spoken to Charlie Tanfield, who's a really cool dude. He's got some great ideas on training.
"We're taking notice of these guys. It's highly likely we'll do some training with these guys, bring them in and see what they've got and I'd welcome that. "We've lost guys over the years - like Geraint (Thomas), (Owain) Doull and (Jon) Dibben - and we're all here as a team representing Great Britain so the more the merrier."