A Plaid source confirmed that the party's finance spokesperson, Heledd Fychan, and Drakeford had met.
They said the figure of extra cash to work with was not precisely known - it was reported to be £230m for day to day services in early November.
Eluned Morgan came under fire from Rhun ap Iorwerth in the Senedd on Tuesday, claiming that thousands of council jobs were on the brink.
"A grim picture emerges of public services teetering on the edge," he said, saying that the spending increase for the NHS amounts to 0.3% in real terms.
Morgan told the Senedd on Tuesday that "our door is open" to Plaid.
"We have invited you to talk to us about the budget... you could help to fix that."
In response, Ap Iorwerth told the first minister to "keep her fingers on the button and keep up with what's going on".
"Plaid Cymru is, first minister, ready to get Wales out of the hole made by Labour," he said.
A later statement from him accused Morgan of being "seemingly unaware that initial discussions had already taken place to understand the budgetary situation".
Ap Iorwerth said Morgan had "completely ignored the public offer by Plaid Cymru to allow a budget settlement to save the NHS and councils from the harm of Labour's original budget tabled".