Plaid leader Ieuan Wyn Jones is set to be named as the Wales' deputy first minister, while Rhodri Morgan remains in hospital after an operation.
Rhodri Morgan and Ieuan Wyn Jones have agreed a coalition deal
The first minister was treated for two partially-blocked arteries and is due to stay in hospital for a few days.
He is expected to ask the Queen to make the appointment and will hold talks with Mr Jones about other cabinet appointments when he has recovered.
Plaid sealed a coalition with Mr Morgan's Labour at the weekend.
Ieuan Wyn Jones is then set to represent Wales at a ceremony to mark the 90th anniversary of the Third Battle of Ypres at Paschendele on Thursday.
Mr Morgan, 67, was admitted to hospital on Sunday night apparently suffering from "gastric problems".
After spending the night in Llandough Hospital in Penarth, he was transferred to the University Hospital of Wales in Cardiff, for an angiogram, which is an X-ray image showing blood vessels.
Two "stents", which are meshes or plastic tubes used to keep blood vessels open, were later inserted in a "standard surgical procedure" and Mr Morgan was conscious throughout.
On Tuesday, Mr Morgan's wife Julie, the Cardiff North MP, said Mr Morgan had told her he felt "terrific" following the operation.
"He looks very well - it is obviously a big shock but things have turned out very well," she said.
"This happened very suddenly, he is very strong and healthy and active. He loves walking and swimming and exercise like that.
"It is very lucky it was spotted now."
Mrs Morgan, who said her husband had seen their children and grandchildren in hospital, added that she could not praise staff at the hospital enough and also wanted to thank well-wishers.
"We have been deluged by people - it means an enormous amount at a time like this."
On Monday, Mr Morgan and Plaid leader Ieuan Wyn Jones had been due to discuss how many cabinet seats - and which posts - Plaid will fill after both parties voted for a coalition deal.
A statement from Business Minister Jane Hutt read: "Rhodri Morgan will not be at the assembly this week as he recovers from the procedure carried out at the University of Wales Hospital.
"I met Rhodri at the hospital and he was in very good spirits."
Dr Clive Weston, consultant cardiologist at Singleton Hospital in Swansea, told BBC Wales that the insertion of two stents should allow Mr Morgan to return to good health.
But he warned the need for the procedure was a clear suggestion that Mr Morgan was a candidate for a heart attack and that he may need to reassess his lifestyle.
Welsh Secretary Peter Hain said: "Rhodri is a remarkably robust and resilient person and I'm sure he will bounce back to full public life sooner rather than later."