The actor, who performed a medley of the singer's hits in character as the delusional DJ for Comic Relief and later incorporated the sketch into his stage show, revealed the Wuthering Heights singer was impressed by his performance.
Appearing on a BBC documentary, he said: "It was fun to do. People laughed and Kate Bush came to the last night of my show to see it when we performed in the West End, she said 'It's so nice to hear all those songs again'."
Coogan, who described Bush's eccentric style as "a gift for satirists", revealed he had tried to tempt her back to performing years ago but failed.
He said: "She rang me to tell me why and it turned into a long conversation about performing on stage, how terrifying it can be, and how she hadn't done it for a long, long time and she felt just a bit scared by the prospect of going out there again."
The tickets for Bush's August comeback sold out in less than 15 minutes as fans went on-line in their thousands to buy them.
The London gigs mark the singer's return to the stage more than three decades after her one and only tour and to the same venue, the Hammersmith Apollo, where she effectively retired from live performances after six weeks on the road in 1979.
She was just 20 when she completed The Tour Of Life with three dates at what was then called the Hammersmith Odeon, after topping the charts with Wuthering Heights the previous year, becoming the first woman to go to number one singing one of her own songs.
For long periods she has largely withdrawn from public life to bring up her son, Bertie.
Her reappearances have been sporadic. Her 2005 album Aerial was her first release for 12 years, although in recent years her work rate has become a little more prolific, with a collection of reworked songs from earlier albums called The Director's Cut as well as a themed album of songs about snow.
BBC4's The Kate Bush Story: Running Up That Hill, which features interviews with celebrity fans including Tori Amos and Jo Brand, will be broadcast on August 22.