Arsenal and Glasgow City are Britain’s remaining two representatives in the competition, while French club Lyon is the favourite to win their fifth consecutive European title.
The quarter-finals arrive five months after the original date of the last 8 draws and months after the last serve of the competition.
All remaining games will be one leg and closed doors, after the first links to two legs in March were postponed due to the coronavirus pandemic.
Lucy Bronze, a side of Lyon, told BBC Radio Five Live: “With the new taste of the festival: a match, the winner takes everything, anything can and there are many strong teams.
“But we all have confidence. We know that if we play our best, we can beat any team.”
Bilbao and San Sebastian welcome the conclusion of the competition, which will have a similar format to the men’s Champions League and Europa League.
The San Mamés Stadium in Bilbao and the Anoeta Stadium in San Sebastian are the two venues, the latter being the last on Sunday, August 30.
There will be no crowds in the matches and all groups will have to comply with strict Covid-19 security and testing protocols.
Arsenal, Britain’s former women’s European champion in 2007, will face French club Paris St-Germain on Saturday (19:00 BST).
Joe Montemurro’s Gunners beat Italian club Fiorentina and Slavia Prague of the Czech Republic in the last 32 and respectively before in the tournament.
Glasgow City is also in eighth place, taking Dane Brondby over the consequences in November.
On Friday (17:00), the Scottish league champions face German club Wolfsburg, who has reached the top European category on 4 occasions since 2013, winning the name twice.
Meanwhile, Atletico Madrid will face national rivals Barcelona on Friday, a matchup between English striker Atletico Toni Duggan and his former club.
The quarter-finals are a match between Lyon champions and German giant Bayern Munich, which starts on Saturday at 19:00.
Lyon is obviously the favorite to retain the title, having won the last 4 finals.
They have been European champions six times and have reached two finals, dominating the festival since 2010.
His team the English Bronze Quartet, Nikita Parris, Alex Greenwood and Jodie Taylor, having signed the latter a short-term contract with the club on August 4.
If Lyon beats Bayern, they will face the winner of arsenal and PSG’s draw in the semi-finals on Wednesday.
The other part of the draw pit pits the winner of the Glasgow City and Wolfsburg adjustment against the winner of Tuesday’s Spanish fit.
Both British clubs have difficult draws and would possibly place their hopes weakened by the fact that some of their rivals have played more competitive football than they did during the summer.
When asked which team would pose the greatest risk to Lyon, Bronze said: “Wolfsburg. They’re on the other side of the draw for us, so if we had to play against them, it would have to be in the final.”
“This is a team where we have already played at the top and have a very smart team. But now you look at all the groups and, to be a cliché, they all have something on them.
“They are obviously all groups to get to the position they occupy.”