The band, fronted by Gavin Rossdale, are busy working on tracks for an upcoming LP and have been using the Foo Fighters singer's Studio 606 in Northridge, California, to get their parts down.
The rockers are collaborating with producer Nick Raskulinecz - who is best known for producing songs for the Foo Fighters and Alice In Chains - and other than letting Bush use his studio, Grohl is not involved in the project.
In a post on his personal Twitter account, Rossdale - who also uploaded a photo of him playing guitar in the studio - revealed: ''The news is out!!! we're in the thick of it with nick r, 5 more songs to sing. getting closer to the finish line. so happy to share!! (sic)''
The 48-year-old musician - who is married to Gwen Stefani - also hinted Bush will hit the road to tour the album.
He tweeted: ''I think we'll tour with the record but what do i know? (sic)''
The as-yet untitled album will be Bush's first release since 'The Sea of Memories' which came out in 2011.
At the time that album had been the band's first studio album for 10 years with previous LP 'Golden State' coming out in 2001.
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Trump's unexpected presidential election victory has caused U2 to re-think a number of their songs for their upcoming 14th album, they say.