The DJ hosted the 5pm-7pm slot on the station for eight years, but was joined by Whiley for an extended 5pm-8pm edition in a shake-up to the schedule in 2018.
The move was met with criticism from listeners, and Radio 2 was forced to issue a response following the backlash, before Mayo later announced his departure to pursue “other radio adventures”.
Mayo told Radio Times that he was told Whiley would be joining the show by his agent.
He said: “It wasn’t a meeting, it was a phone call from my agent saying she’d had a visit from (Radio 2 controller) Lewis Carnie who’d said, ‘Co-presenting is the future.’”
He added: “I was concerned that they’d pluck a co-presenter out of a bag somewhere, and I said it needed to be Jo. I’ve known her for a long time, and our families had been on holiday together.”
Asked if he believes Radio 2 really thinks co-hosting is the future, Mayo said: “No. My guess is that there was genuine pressure from the top about improving the number of women in daytime.
“And they looked at the radio I do and the fact I’ve worked with Mark (Kermode, on their BBC Radio 5 live film show) for many years, and thought, ‘He might at least give it a go.’
“Because if you suggested it to ... some of my former colleagues, they know it wouldn’t have worked.”
Mayo said there was never a sense that if it had not worked it would be reversed, adding: “They’d invested too much political capital in the change.”
He has since landed a presenting role at new classical music radio station Scala Radio, which will be on air from March 4, but said that Chris Evans offered him a job at Virgin Radio when he also exited Radio 2.
Mayo told the magazine: “He rang me and said, ‘Do you want to work here?’ I said, ‘I’m already spoken for.’ He said, ‘I’ve got an audience of 8.7 million.’ I said, ‘Where I’m going we haven’t got any listeners at all. We’re starting from zero!’”
Assessing the final result of the shake-up at Radio 2, which has resulted in Zoe Ball hosting the breakfast show and Sara Cox hosting Drivetime, Mayo said: “It’s not the way I’d have designed it.
“The show that Drivetime became was the most perfect reflection of who I was as a person and gave Radio 2 the highest listening figures it ever had. I don’t think enough thought had gone into the impact that change would have.”