Dublin North TD Mr Reilly said he will be "pushing very hard" around the Cabinet table for Metro North.
Referring to Mr Varadkar's position as Transport Minister and a TD for Dublin West, Mr Reilly said "you couldn't hope for better in terms of driving this project forward".
However, when contacted, Mr Varadkar's spokeswoman told the Herald the Government's position will only be clear when they have had time to consider the project.
"They [the ministers] were only really appointed on Wednesday of last week and then the ministers of State were appointed on Friday," she pointed out.
"Our minister is currently in India [for St Patrick's Day celebrations]," she added.
The spokeswoman indicated that no decision has been made either way on whether to sign off on orders allowing for preliminary works on Metro North.
"Currently what the situation there is that the minister is familiarising himself with his brief at present and the Government has yet to consider it. That is where things are," she said.
She added that "there is mention in the Programme for Government of a commitment to high speed public transport".
However, the Government has to consider it and "then make a decision on it at that stage", the spokeswoman said.
Mr Reilly said: "[Metro North] fits in very well in terms of creating jobs and providing infrastructure to ensure we remain competitive."
Businesses and residents in Dublin North have been calling for construction on the 18km Dublin Airport link, which will cost €2.5bn, to begin.
Fingal councillors put pressure on the previous government to immediately begin construction of Metro North.
Prior to stepping down as Transport Minister, Fianna Fail's Noel Dempsey said whether the project goes ahead or not "is a budgetary matter".