The Carlow-Kilkenny Deputy approached Stephen Donnelly at this week's parliamentary party meeting and tried to give him the dummy, but the Minister refused to take it.
Both politicians have been engaged in a long-running spat.
John McGuinness has repeatedly called for the Minister and the Department of Health Secretary General Robert Watt to go before the Oireachtas Finance Committee over the senior civil servant's €81,000 pay increase.
John McGuinness says he had his grandchild's soother in his pocket at the meeting:
"I spoke to Stephen Donnelly given the difficulties we've had and the exchanges we've had and as a point of humour, I offered him a soother to see would that calm matters between us but I'm afraid my attempt at humour may not have worked. That's what happens when you're looking after your grandchildren, you tend to put these items in your pocket from time to time."
