He said "we've yet to see anything that remotely approaches" an alternative to the Northern Ireland backstop agreement
The Taoiseach has said the Government will need to question whether there will be a Brexit withdrawal agreement at all if there's no substantial progress by June.
The final deadline for an agreement between the UK and EU is October, but European leaders are set to review progress next month.
As the Brexit negotiations continue, Leo Varadkar is meeting Theresa May on the sidelines of an EU-Western Balkans summit in Sofia today.
Speaking in the Bulgarian capital ahead of that meeting, the Taoiseach said: "By June, we need to see substantial progress - as the Tánaiste and myself have seen on many occasions.
"The deadline, of course, for the withdrawal agreement is October - but if we're not making real, substantial progress by June, then we need to seriously question whether we're going to have a withdrawal agreement at all."
He also said he has yet to see anything 'remotely approaching' an alternative to the so-called 'backstop' agreement to avoid a hard border.
The 'backstop' refers to an earlier deal reached between the UK and EU in December, saying a “common regulatory area” will be established in Northern Ireland following Brexit if no other solutions to the border issue can be found.
Mr Varadkar said: "We stand by the same position that we've had for a very long time now - that there can be no withdrawal agreement without the backstop, and we need that backstop to ensure there's no hard border.
"If the United Kingdom wants to put forward alternatives to that - whether it's an alternative text to the backstop, or whether it's some sort of alternative future relationship between the UK and the EU - we're willing to examine that."
However, he stressed: "We need to see it written down in black & white - we need to know that's it's workable and legally operable... and we've yet to see anything that remotely approaches that."