Seán Canney is still considering his options as his future in the Independent Alliance remains in doubt.
Some members of the Alliance had hoped that Mr Canney would have made his position clear at the weekend.
The Galway East TD is unhappy that the group is unwilling to rotate the Minister for State role at the Office of Public Works for a second time.
The position is currently held by Kevin 'Boxer' Moran who has received the backing of his colleagues to stay in the job until the next election.
Mr Canney held the role for the first year of the current Government before it rotated to his Alliance colleague.
He held a private meeting with Taoiseach Leo Varadkar last week.