The Hoops, who beat St Mirren 5-1 in the fifth round in the east end of Glasgow at the weekend, travel to Tynecastle.
Coincidentally, Ange Postecoglou’s men are due to face Robbie Neilson’s side at Parkhead in the league in the midweek before the tie.
The champions beat Hearts 2-0 in the first league meeting of the season at Parkhead in August and were then involved in VAR’s debut in the capital where the Hoops won 4-3 with Greg Taylor claiming the points-clincher in October.
In the other ties, Inverness Caley Thistle face Kilmarnock, the Ibrox side are at home to Raith Rovers while it’s Darvel or Falkirk, who play tonight, versus Ayr United.
The last-eight confrontations are due to take place on the weekend of March 11/12.
Celtic last won the competition in December 2020 when they overcame the Edinburgh outfit in a dramatic penalty-kick shoot-out following a 3-3 draw following extra-time.
Ryan Christie, Odsonne Edouard, with a penalty-kick, and Leigh Griffiths, in the added-on period, were on target for Neil Lennon’s men.
However, the Edinburgh club fought back bravely to level the scores and force spot-kicks. Craig Gordon denied former team-mate Christie, but Conor Hazard provided heroics of his own with two excellent saves.
THE GLORIOUS TWELFTH…Kristoffer Ajer lashes the deciding penalty-kick past Hearts keeper Craig Gordon for Celtic’s Scottish Cup winner in December 2020. The goal sealed the quadruple treble and the club’s twelfth successive domestic honour.
It was all down to Kristoffer Ajer with the decisive kick and the big Norwegian fairly belted the ball into the net to seal the Hoops’ phenomenal quadruple treble and twelfth consecutive domestic trophy.
Ange Postecoglou’s men, of course, will be back at Hampden a week on Sunday for the Viaplay League Cup Final against Michael Beale’s Ibrox outfit.
They go into the encounter as holders of the silverware – then known as the Premier Sports Cup – when they beat Hibs 2-1 in December 2021 with two second-half goals from Kyogo Furuhashi.