The spat began after a secret recording emerged of interim leader Alex Rowley backing Richard Leonard for the top job, despite claiming to be neutral.
During the private chat with a student at the Labour conference, he admitted Mr Leonard was being groomed for the leadership even before Ms Dugdale’s shock resignation.
He said: “Any private discussions we were having, we were very clear that… we didn’t think it would happen before 2021.
“We, privately, didn’t believe Kezia would be there in 2021. But not right now. It came as a surprise to us.
“So our view was that Richard was the best person and, therefore, we should go with that plan. But he has now to get elected, of course.”
Fellow MSP Jackie Baillie, who is backing moderate candidate Anas Sarwar, said: “Kez was elected with a huge majority and it will infuriate members to learn some MSPs were working to undermine her. Richard must answer questions about his role in this plot.”
A spokesman for Mr Leonard’s campaign said: “If there were any attempts to undermine Kezia, they did not involve Richard.”