Murray won gold at the Rio Olympics a week ago. He defeated Canada's Milos Raonic 6-3, 6-3 on Saturday in a semi-final match that was affected by rain, reports Efe.
Cilic advanced to the final, defeating Bulgaria's Grigor Dimitrov 4-6, 6-3, 7-5 in a contest that was also delayed by rain here on Saturday.
Murray is the favourite to win his third title at Cincinnati. The World No.2 has a career head-to-head record of 11-2 against Cilic.
The most recent meeting between the players ended with Murray beating Cilic in three sets at Queen's Club earlier this summer.
On the women's side, the Czech Republic's Karolina Pliskova, the World No.17, will take on Germany's Angelique Kerber, the second seed, in the championship match.
Pliskova has upset Spanish World No.3 Garbine Muguruza 6-1, 6-3 in the semi-finals on Saturday.
Kerber the silver medallist at the Rio Olympics, beat Romania's Simona Halep 6-3, 6-4 in the other semi-final match.
