Only three other English clubs – Leicester, Wasps and Saracens – have achieved such a feat, but Exeter, who were in the second-tier Championship 10 years ago, are now hunting both prizes.

"We obviously don't want to get too ahead of ourselves, but it's something we really want," Exeter and England wing Nowell said.

"We have been working extremely hard, and now is the time to start enjoying these big games. We've got a lot of experience over the last few years of playing in them.

"It's cool being in the Premiership, but we want to start winning stuff playing in these big games. We want to be in European quarter-finals, semi-finals and finals."

Exeter featured in the last four Premiership finals at Twickenham, and Nowell added: "A taste of those finals has only added to that. Exeter boys being greedy, we want a bit more.

"The next step for us is the Champions Cup, and we are in a very good position this year. A couple more hurdles to go."

Cornishman Nowell was just 17 and on Redruth's books when Exeter were promoted to English rugby's top flight in 2010.

But he soon became a Chiefs player and proved instrumental behind Exeter's rise to the Premiership title three years ago and becoming Twickenham regulars.

"If you had said to me back then – 17 and still at college – that I would be in a European Cup semi-final at Sandy Park against Toulouse, it would have been surreal," he added.

"I wouldn't have believed you. I thought I would have been on a trawler, fishing with my old man."

Exeter's previous European campaigns have produced a solitary quarter-final appearance – against Wasps in 2016 – which gives this weekend added significance.

Nowell said: "We've always let ourselves down in this competition.

"You need to win every game, you can't rely on other people and you can't rely on other results to go your way.

"That's what we have done well this season. We haven't actually changed anything in terms of our mentality and how we attack the games. Results have gone our way a little bit."

The coronavirus pandemic and current restrictions mean a behind-closed-doors setting at Sandy Park on Saturday, but it should not affect the quality of an eagerly-awaited clash between two in-form teams.

And among individual battles littered across the pitch, none is more eye-catching than Nowell's with Toulouse try machine and South African World Cup winner Cheslin Kolbe.

"He is obviously going to be a handful," Nowell added.

"We've spoken about him, and we are going to have to look out for him on the field, soak up what he has got to give, but also try to fire a few shots ourselves.

"He is not the biggest of guys, but he is extremely quick and strong for his size. You can't give him space, because that is when he's at his best."