Peer, who was unable to compete in the tournament last year after being denied an entry permit to Dubai, reached the last four when China's Li Na retired with back injury when the Israeli was leading 7-5 3-0.
Having expressed her support for Peer during the presentation ceremony last year, Williams was looking forward to playing her.
"Yeah... that's life, how things turn out," she said. "I'm actually really looking forward to both of us really playing in our top level."
Due to security concerns Peer has played all her matches this week on a side court and that will remain the case for her clash with Williams, who accepted the situation.
"How I feel about it is, I think whatever is best for everyone," Williams told reporters. "If this is the best decision then I support it."
Azarenka defeated 12th seed Vera Zvonareva, who won the Pattaya Open in Thailand last week, 6-1 6-3.
Radwanska had much more of a challenge in ending the run of Russian qualifier Regina Kulikova 3-6 6-4 6-3.
After taking the first set, Kulikova held two break points in the second that would have left her serving for the match at 5-4.
But Radwanska broke with a backhand volley to take the set and after an early exchange of breaks in the third earned the decisive break to lead 4-2 when Kulikova made a forehand error.
"She was very consistent. She was moving well, hitting the ball. Sometimes she was like a wall," said Radwanska. "No mistakes at all. For sure, she was on fire here on this tournament."
(Editing by Alison Wildey)