Italian Sinner has reached the finals of the past three Grand Slam events, winning two of them. At 13:30 BST, he will open play on Centre Court against Spaniard Pedro Martinez, who is ranked 52nd in the world.
Djokovic, 38, is making his 20th appearance in the men’s singles at Wimbledon and will aim to make it to the fourth round for the 17th time.
He is third on Centre against fellow Serb Miomir Kecmanovic, who has equalled his best-ever run at the tournament.
In between those two matches, world number four Swiatek takes on former Australian Open runner-up Danielle Collins.
Seventh seed Andreeva plays in the first match on Court One (13:00 BST) against Wimbledon debutant Hailey Baptiste, followed by Krejcikova’s tie against 10th seed Emma Navarro of the United States.
Men’s 10th seed Ben Shelton, having needed just over a minute to wrap up his second-round win on Friday, rounds things off on Court One against Hungarian qualifier Marton Fucsovics.