The 'Good Vibrations' hitmakers insist they never sacked frontman Brian - who briefly rejoined the band for their 50th anniversary tour and new album 'That's Why God Made The Radio' last year - claiming it was he who didn't want to continue touring with them.
The band's Mike Love told the Daily Star newspaper: ''I don't know how that sacking controversy started. I'd love to work with Brian again.
''The anniversary tour was originally 50 dates, and got extended to 73. At that point, Brian said: 'No more dates for us, please.'
''So once we finished those 73 shows we went back to the line-up of the band before he rejoined.''
Mike owns the rights to the Beach Boys name, and reunited with original members Brian, Al Jardine and David Marks for their anniversary shows, but has since gone back to performing with his own line up of the band.
The Beach Boys performed at Barclaycard Presents British Summer Time in London's Hyde Park on Sunday (07.07.13), but Brian was noticeably absent.
However, Mike would love to write more songs with Brian, his cousin, who was the band's main songwriter in the 60s, behind tracks including 'Surfin' U.S.A.' and 'California Girls'.
He said: ''I'd very much like to get in a room, just him and I, to write more songs. We've always had a special chemistry, which has helped craft some fantastic music and given us a tremendous amount of success. We didn't write together on last year's album, and I'd like to do that more than anything.''
However, chances of a reunion are looking slim as when asked if he would get back with The Beach Boys last year, Brian said: ''No, I don't think so. Doubt it.''
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Pratchett died aged 66 in March 2015.