The Government has faced sustained criticism and pressure over its appointment of Katherine Zappone as UN special envoy, with Mr Coveney subject to scrutiny over his involvement in the affair.
The motion, which will be filed this morning, says the Minister failed to explain the handling of Ms Zappone’s appointment in a credible manner.
Last week, Sinn Féin said it would consider tabling a motion of no confidence against the Minister if the Taoiseach did not sanction him.
Party leader Mary Lou McDonald said Mr Coveney’s handling of the crisis was “not the standard expected” of a government minister.
With the Dáil returning after its summer recess on Wednesday, one of its first pieces of business will be to deal with the no-confidence motion.
At the Fianna Fáil think-in ongoing in Cavan, Taoiseach Micheál Martin expressed confidence in Mr Coveney, who is in New York chairing a meeting of the UN Security Council.