Harlequins scrum-half Danny Care says it would be "miraculous" if an English team won the Investec Champions Cup this season.
Quins are one of five Premiership clubs through to the knockout stages of the competition, but only Northampton Saints earned a home draw in the round of 16.
The Twickenham-based side return to league action away to rivals Saracens on Saturday and also travel to face Bath on 29 March before tackling four-time Champions Cup winners Leinster - beaten finalists the last three years - in Dublin on 5 April.
Saints and Harlequins reached the semi-finals of Europe's premier cup competition last year, a feat former England international Care described as "remarkable".
"These are the types of games you still want to be playing in; obviously no-one gives us a chance in hell but we'll give it a crack," the 39-year-old told BBC Sport.
"I think it'd be miraculous if an English team can get their hands on that at the moment, with the way the tournament is, to go up against these French and Irish superpowers. Last year for us and Northampton to get to a semi-final was remarkable.
"If one of us could do it again this year it would be nothing short of a miracle, but we'll try our best and see what happens."
Care has played more than 250 times for Harlequins
The tournament has been won by an English club on 10 occasions since it was launched in 1995-96 under the previous name of the Heineken Cup.
Since Exeter Chiefs beat Racing 92 in the final at Ashton Gate in 2019-20, the trophy has been claimed by a French club in each of the subsequent four years, with no English finalists in that time.
Harlequins have never won the tournament in their history, while London rivals Saracens are the most successful English club in the competition with three titles, the last in 2019.
Sarries visit three-time champions Toulon in the last 16, while Sale Sharks face a trip to holders Toulouse.
Leicester Tigers visit Glasgow Warriors and Northampton host Clermont Auvergne at Franklin's Gardens in the first of the last-16 ties.
Harlequins are currently sixth in the Premiership table, three points behind fourth-placed Leicester with seven matches remaining.
Care announced in January he would remain with Harlequins next season for his 20th year with the club.
He has won two Premiership titles with the club and said he would love to add to his collection before hanging up his boots.
"[I'm] Not [planning on playing for] much longer. I'm still really enjoying my rugby, I love the club, I always said I'd never pack it in until I didn't feel I could help the team, or I wasn't enjoying it," he added.
"I'd love to help the club lift another trophy before I stop. Whether that be this year or next year, I'm not sure but I'll try my best to help these young lads reach their goals and reach their dreams."