The minister has been commenting as controversy continues over Máire Whelan's nomination to Court of Appeal
Shane Ross says he has made it clear that he wants the system for appointing judges reformed.
The comments come as controversy continues over the nomination of the former attorney general as a judge.
Máire Whelan was appointed to the role during Enda Kenny's final Cabinet meeting as Taoiseach.
The role at the Court of Appeal carries a salary of €180,000 a year.
Her name was put forward by the former justice minister, Frances Fitzgerald, after the Judicial Appointments Advisory Board was unable to suggest any candidates.
Opposition politicians have sharply criticised the process, while the new Taoiseach has insisted the correct procedures were followed.
Pressure is now mounting on Shane Ross - an independent member of Leo Varadkar's new cabinet - to come through with his previous promises of reform.
It is reported that the Transport Minister raised concerns about the process during the cabinet meeting in which the nomination was made.
Speaking at today's Luas Cross City testing, Minister Ross said he would address the matter at cabinet on Tuesday - and insisted that he "would not have allowed something like this to happen without an intervention."
He also noted that legislation to reform the appointment process will come before the Dáil next week or the week after.
Minister Ross told reporters: "The Independent Alliance made it absolutely clear all along that [...] we don't like the process of appointments.
"It's no coincidence, I suppose, for many years every time a judge has been appointed there's been some sort of political row. That's what we want to end."