Cilla, who died earlier this month in Spain, is said to have been "thrilled and excited" about the production and had meetings with theatre producers before she passed away.
The musical will chart the rags-to-riches tale of how Cilla rose from a nightclub cloakroom attendant at Liverpool's Cavern Club, to become showbiz royalty and entertain the nation every Saturday night.
Cilla's rep Nick Fiveash confirmed: "Cilla was thrilled and excited at the idea, and was looking forward to its development. Her manager, son Robert Willis, had been in continuous talks with a West End producer regarding early stages of planning, but obviously these are now on hold for the time being."
A source told The Sun that Sheridan Smith, who played the TV legend in a recent ITV biopic, could make a return in the musical.
The insider said: "Sheridan's portrayal was wonderful. She's a great singer and more than capable of making the role her own."
This news comes days before Cilla's funeral, which is due to take place on Thursday. The Blind Date presenter died of a stroke after falling and hitting her head at her Spanish villa on 1 August, aged 72.
Cilla's sons, Robert, Ben and Jack released the information after receiving conclusive results of the autopsy from Spanish authorities.
They said in a statement: "We have been deeply touched by all the kind messages of support from her friends, fans, the public and media.
"We would like to thank everyone, especially the people of Liverpool. The tributes and condolences have really helped us through these difficult times."
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