Federer is through to the semi-final stage after beating Alexander Zverev in three sets, 7-6, 5-7, 6-1.
But before finding out who he will face in the next round, Federer faces Cilic on Thursday in the one final round robin match.
The Croat cannot qualify for the latter stages having lost both opening matches to Zverev and Jack Sock.
However, Cilic will no doubt be keen to end the season on a high by recording a win over the world No 2.
RELIVE ALL THE ACTION FROM ROGER FEDERER’S WIN OVER ALEXANDER ZVEREV HERE
Federer could be forgiven for wanting to reserve some energy for his semi-final match scheduled to take place in either the afternoon or evening session on Saturday.
But Peter Fleming, who won seven Grand Slam Doubles titles in the 1970’s and 1980’s, expects Federer to keep his foot on the gas.
“I expect him to play near his best,” said.
“I’m not sure that emotionally he will get too involved in that match and if things go the wrong way I don’t think he will be that concerned.
“But every time he walks on the court he wants to play his best tennis and he’s in a nice rhythm and will want to solidify that rhythm.
“He did play a terrible game early in the second set to allow Zverev back in so he will want to eliminate that so it’s almost like a day of practice for him.”
Former British tennis star Greg Rusedski was impressed at how Federer fought back after a dip in form to see of Zverev.
“He is the greatest for a reason in my opinion just because he knows how to get the job done, he knows how to change his tactics, he’s done it all,” he said.