From what's been reported over the years:
Cher was very close to taking the role on Broadway, with her friend John Barrowman playing 'Joe Gillis' (that was part of her negotiations for the role, and Barrowman was 100% behind it). In the end, the deal fell apart. According to Cher (years later, in an interview in London) she said "He simply couldn't afford me" (referring to ALW) when asked what was the deal breaker. According to a spokesperson for RUG, Cher had released her (new) album "It's A Man's World" stateside the last week of June, 1996 and could not commit to a schedule of rehearsals - she was busy with promoting her new album around the country. in her contractual agreement with WB Records. (Buckley's replacement would be taking over the first week of September, it would never work out if Cher missed rehearsals in July and August).
Before signing on with Elaine Paige, it was said ALW offered the role to Diana Ross (she only wanted to do the Thursday, Friday and Saturday performances and have her understudy fill in the others) Olivia Newton-John, Barbara Eden, Dixie Carter, Shirley Jones, Jennifer Holiday, Joan Collins, Tyne Daly and Bernadette Peters. Daly said she was 'interested', but after talking to Betty Buckley about the physical demands of the role (the actress playing the part would climb up and down nearly 1,000 stairs by the end of the week's performances), she declined. Supposedly, Peters declined for the same reasons.
As for Liza, let us not forget - shortly after she married David Gest in 2002, they announced to the press she was going to star as 'Norma Desmond' in the movie version of the musical. Gest said it was a done deal, everything was negotiated and signed off, and production was to start 'within months'. . ALW said none of that was true. 21 years later, I guess ALW was telling the truth.