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Nick Cushing's side will host the Swedish champions at the Academy Stadium on Wednesday 21 March at 7pm GMT before the away leg will take place a week later at Linkoping Arena on Wednesday 28 March at 6pm CET (5pm BST).
Should the Blues progress to the last four, they will face either Lyon or Barcelona on 21 or 22 April (home) and 28 or 29 April (away).
A first league title in the 2016 season, which was accompanied by a Continental Tyres Cup and a Champions League debut, clinched the Blues’ second qualification to the competition.
The Blues reached the semi-finals in their maiden campaign, defeating Zvezda Perm, Brondby IF and Fortuna Hjorring before falling to eventual competition winners Lyon. To reach this stage of this season's competition, they triumphed 6-0 on aggregate against SKN St Polten before defeating LSK Kvinner 7-1 over two legs in the Round of 16.
Damallsvenskan outfit Linkopings defeated Apollon Limassol and Sparta Praha to progress to the last eight, having have reached the quarter-finals on three occasions (2011, 2015 and 2017) - their best performances in the competition.
Former Blue Kosovare Asllani rejoined the Swedish side in August.
The Champions League final will be held at the Valeriy Lobanovskyi Dynamo Stadium in Kiev, Ukraine on Thursday 24 May 2018.
Ticket information for the quarter-final tie with Linkopings will be revealed in due course.
Last four tie to be played on the weekend of 13/14 January.
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