It follows the recent leaks controversy
The party says the Tánaiste has yet to put forward a credible reason for giving a confidential GP contract to a friend of his in a doctors union.
Tánaiste Varadkar spent two hours in the Dáil defending himself on Tuesday.
He said the contents of the IMO contract were very much in the public domain by the time he gave a copy of the deal to his friend Dr Maitiu O Tuathail, who at that time headed a rival doctors union.
Both Fianna Fáil and the Green Party have publicly backed Leo Varadkar's position.
However it's caused dissent in Fianna Fáil in particular, with a number of TDs unhappy at the position taken.
A spokesperson for Leo Varadkar said this afternoon the no confidence motion shows Sinn Féin are not interested in the truth, only political mudslinging and attacking the government at a time of national crisis.
The motion will be debated in the Dáil next Tuesday.
