And he invited her to come and watch the Blues train in the future.
Kayley survived an eight-hour heart and lung transplant at London's Great Ormond Street hospital, stunning doctors with her incredible progress.
Since she has been back in Liverpool, Kayley has led the ECHO's campaign to save Alder Hey after benefiting from treatment there all her life.
A spokesman for the club said: "The original plan was to bring Kayley to Bellefield, but with one thing and another we couldn't find a suitable date - so Duncan suggested that we visit her at home.
"We've kept in touch with Kayley's mum and her strength and bravery have impressed everyone at the club.
"She was delighted when Big Dunc knocked on her front door and as soon as she is up to it, we will be bringing her to the training ground to meet the rest of the lads."