Deputy Lawless has been a TD for Kildare North since 2016.
Kildare TD James Lawless is being considered as a replacement for Robert Troy's role.
The Taoiseach says he'll consider the 'ability' of his colleagues, when deciding who will take over Robert Troy's junior ministerial role.
However, it's expected Mayo TD Dara Calleary will be handed the enterprise portfolio, having stepped down as agriculture minister in 2020 in the wake of Golfgate.
Cavan/Monaghan TD Niamh Smyth is reportedly also being considered.
However Michael Martin refused to be drawn on questions on the appointment: