"During that period I was asked to join Deep Purple, Van Halen and Little Feat, all within a few months; I was the flavour of the month," he wrote in his 2017 book Working Class Man.
"I came back from the studio on the final day and Jane (his partner) was waiting to go to the shops to buy some things on our last day there and told me to look after Mahalia and EJ (his children).
"As she left she says 'By the way, Eddie Van Halen rang for you'.
"So I call him back and he asks me to come over to his house because he wanted to ask me something.
"I explained I couldn't leave the house because I was babysitting, and half an hour later, there's a knock at the door and these two guys come in very worried-looking and Eddie says they're looking for a singer, David Lee Roth had left the band," Barnes explained.
"I told him I didn't really want to join another band, I was just starting my solo career and I'd like it see that through. But I was really flattered, I really like Van Halen.
"I got word when Sammy Hagar left the last time they were trying to get hold of me again."
Barnes today paid tribute to Eddie Van Halen on Twitter after learning of the musician's death, writing: "Was lucky enough to meet Eddie in the mid 80s when he asked me if I was interested in joining Van Halen.
"I'd just started my solo career so the timing wasn't right but still to this day, it's an honour to have been asked to play with such a legendary rock band. RIP Eddie."
