The 'Do I Wanna Know?' hitmakers want some special guests at their massive shows in Hyde Park, and though the 'Purple Rain' hitmaker was at the top of their wish list, they didn't ask him as they knew he wouldn't accept their request.
Bassist Nick O'Malley said: ''We were talking about bringing Prince in to do the high backing vocals - they'd probably be low backing vocals for him anyway.
''But we've never met him and I doubt he'd be up for that. For the size of the show though, you really should do something.''
The group admits they could have headlined such big gigs - which will see them perform to 50,000 people over the course of the weekend - earlier in their career, but think they will give a better performance because of the way their latest album, 'AM', has connected with fans.
Frontman Alex Turner added to NME magazine: ''Probably in terms of selling tickets, we could have done something like this before but we weren't as on fire then as we are now.
''We couldn't do what we're doing now without that record. Had we done it before, I think it would have, in some way, still have been based on the first album and its success. To some extent, everything is built on that, but now, it's the new record most people want to hear.''
This Doctor won't be saying 'goodbye' in the same way as those who have left the series in recent years.