Zverev returns to the O2 Arena after his debut last year in which he won his first match - which also happened to be against Cilic - but ultimately failed to qualify from the round-robin stage.
The highly-rated German has had a solid year overall with three titles to his name - including a third Masters 1000 trophy - but he has suffered some heavy losses in recent tournaments that will have dented his confidence.
Since losing his first ever meeting with Cilic in 2015, Zverev has gone on to win their last five encounters so he holds the psychological edge in this rivalry.
Cilic makes his fourth appearance at the finals but this tournament has not been a happy hunting ground for him; he has finished bottom of his group on each occasion and has managed just one win in nine attempts.
The Croat's form has generally been poor in the hard court stretch since the US Open with a number of early exits but he was much improved in the recent Paris Masters, losing to world number one Novak Djokovic in the quarter finals in which he took a set off the Serb.
His losing record against Zverev perhaps doesn't tell the full story as three of his defeats have come via a deciding set so he won't be too deterred by that record.
Both players will be looking to get out of the group for the first time in their career when they face off in what will be a repeat of their opening match at the O2 last year. On that occasion, Zverev won in three sets and a repeat scoreline here would not be a huge surprise.
Backers should be aware that Zverev has looked a little out of sorts lately, and also that Cilic will have regained some confidence after taking a set off Djokovic in Paris recently, but when you look at the Croat's poor record in the tournament, you have to favour Zverev. It has also been noted that the court is playing slower than in recent years, so that will also go in the German's favour. Zverev in three sets.