The Blur and Gorillaz frontman - who is joined in the supergroup by The Clash's Paul Simonon, The Verve's Simon Tong and afrobeat drummer Tony Allen - is juggling his live commitments with recording sessions in the UK on the follow-up to the band's self-titled 2007 debut.
He told Consequence of Sound: ''I'm on tour in Europe doing festivals, but I'm coming home in between them [to finish the record].
''I'm working all weekend doing festivals and then come home Monday, Tuesday, and Wednesday -- that should be a weekend. But because I've stupidly started and want to make this record right, I don't have any weekends.''
After releasing a new Gorillaz album, 'The Now Now', already this year, the 50-year-old singer - who hasn't performed with The Good, The Bad, and The Queen since they did a one-off show in 2011 - joked he's worried fans will get tired of him.
He said: ''What I would really like never to do is for people to get sick of me, because I was putting out too much stuff. If that ever happens, like you do to elderly relatives, put your arm around me and wheel me off please.''
Damon's update came after producer Tony Visconti previously spoke of how long he'd been working on the record.
He said: ''In the middle of 2017, I started working with Damon Albarn.
''We're about two thirds of the way through and taking a break, as Damon is off on a Gorillaz tour, but we will resume in April and it will be probably be out before next Christmas.''
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