Medvedev became the first player through to the semis with a 7-6(7), 6-4 victory over Zverev, and the German now needs the third seed to beat Alcaraz.
Alcaraz, who is looking to become the youngest ATP Finals champion since Pete Sampras in 1991, eased to a 7-5, 6-2 win to revive his hopes in Red Group after he had opened with defeat to Zverev.
Zverev and Alcaraz have entered the final round of group play at 1-1. Zverev will next face Russian Andrey Rublev.
"I've never won a second round-robin match at this event and I won the tournament twice ... that obviously gives me hope," Zverev told reporters.
"On Friday, I'll be the number one Daniil Medvedev fan there is on this planet, for a change," he said with a smile. "We'll see how it goes.
"It's a little bit out of my hands ... I have to be focused and be ready ... ready to beat Andrey."
Medvedev said he understood why Zverev wants him to win, but it would not be easy against the two-time Grand Slam winner Alcaraz.
"It's normal. I would be the same." Medvedev said.
"I'm going to try my best to play Carlos. It is not easy. But here, fast court, so it can be interesting.
"The moment you relax and say to yourself 'maybe this match I can go easier', you can lose all the rhythm. That's how tennis is."
