It has a credit-crunch theme - with panto actors going on strike after the Princess gets kidnapped.
The Angels crooner agreed after Paddy chatted to Robbie's pal Jonathan Wilkes about doing a spoof one-off performance.
Paddy told TV Biz: "I thought it would a good idea to do something a bit different.
"We all got talking about songs and Robbie said he's going to write one."
Bolton comic Paddy, 36, is not banking on the chart-topper joining him on stage in Manchester.
He joked: "It would be like Jesus Christ walking on. There's only room for my ego on that stage."
Paddy's dating show Take Me Out returns to ITV1 later this year for a second series.