The two players haven't met since Murray was thrashed by Federer at the ATP World Tour Finals in London last year.
The British No 1 has enjoyed a huge upturn in form since that day, losing just six of his matches this year.
By the time the pair take to Centre Court, they will know which player will await them in Friday's final.
Defending champion Novak Djokovic is scheduled take on Richard Gasquet in the first match on Centre Court.
But when is everyone else playing? Here is the full running order for July 10...
Centre Court - 1pm start
(1) Novak Djokovic (SRB) vs (21) Richard Gasquet (FRA)
(3) Andy Murray (GBR) vs (2) Roger Federer (SUI)
No.1 Court - 1pm start
(1) Martina Hingis (Swi) & Sania Mirza (Ind) v (5) Raquel Kops-Jones (USA) & Abigail Spears (USA),
Jeremy Bates (Gbr) & Chris Wilkinson (Gbr) v Joakim Nystrom (Swe) & Mikael Pernfors (Swe),
(1) Mike Bryan (USA) & Bethanie Mattek-Sands (USA) v (7) Leander Paes (Ind) & Martina Hingis (Swi)
No.2 Court - 11.30am start
Albert Costa (Spa) & Fernando Gonzalez (Chi) v Jamie Baker (Gbr) & Fabrice Santoro (Fra),
(4) Timea Babos (Hun) & Kristina Mladenovic (Fra) v (2) Ekaterina Makarova (Rus) & Elena Vesnina (Rus),
Jana Novotna (Cze) & Barbara Schett (Aut) v Chanda Rubin (USA) & Sandrine Testud (Fra),
Robert Lindstedt (Swe) & Anabel Medina Garrigues (Spa) v (5) Alexander Peya (Aut) & Timea Babos (Hun)
Are you looking for a great place near you to watch the tennis? Here's where all of the best big-screens are in west London.