Under the plan, all those holding Irish citizenship would be able to cast their votes at Irish embassies.
Mr Varadkar said including emigrants in presidential elections would help build closer links with the diaspora.
"I support allowing Irish citizens all over the world to vote in presidential elections because the President should be the President of the Irish nation and not just the Irish State," he said.
The issue will be considered by the Constitutional Convention, set up to make recommendations on updating the 1937 Constitution. The Government will then decide if it will hold a referendum.
However, the Constitutional Convention will not be looking at whether to allow emigrants to vote in general elections which Mr Varadkar said he was in favour of "in principle".
"If the . . . franchise is extended we will not have the ridiculous situations where former President Mary McAleese, whose allegiance to Ireland is unquestionable, was denied the right to vote for so many years because she was born and lived in Belfast," he said.