Luxembourg's Muller, seeded 16, may have caused one of the biggest shocks of the championships by vanquishing Rafa Nadal, but nonetheless goes into the match as the underdog.
Croatian seventh seed Cilic has won their two previous encounters, including on the grass at London's Queen's Club last month, and he has yet to drop a set at Wimbledon this year.
Both men cut imposing figures, with Cilic a towering 6ft 6in tall and Muller 6ft 4in. In awesome displays of power-hitting, they have fired a combined 174 aces over the net at this year's championships, and more than 460 winners.
"You have everywhere advantages and disadvantages," Cilic said of his size and reach after crushing Roberto Bautista-Agut in the last 16 with his pounding serve and thumping forehand.
"Tennis is a game that is extremely complex and you can play it any way you want, so you have to use your advantages well."
Cilic, a U.S. Open champion, will be looking to banish painful memories from the same stage last year, when he snatched defeat from the jaws of victory by squandering a two-set lead and three match points against Roger Federer.
Serve-and-volleyer Muller, who at 34 is six years older than Cilic, is aiming to reach his first grand slam semi-final.
The Luxembourger will hope to have enough left in the tank after a near-five hour clash with Nadal, which ended 15-13 in the fifth set.
Asked how he felt after that match, he said: "Tired."
He added, smiling: "I'm just glad it's over."
(Reporting by Pravin Char; editing by Ken Ferris)
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