The Irish prime minister is "not optimistic" enough progress will be made in the Brexit talks to allow the the UK and the EU to discuss a new trade relationship by mid-October.
The EU says talks on a new deal can only begin when all 27 EU states are satisfied sufficient headway has been made on the UK's withdrawal terms.
Leo Varadkar made the comment on Friday at a meeting of his Fine Gael party.
He was supported by his Foreign Affairs Minister Simon Coveney.
"I'm not optimistic that it will be possible to come to the view in October that we're able to move onto the next phase of talks," said Mr Varadkar.
"As of now, enough progress hasn't been made, but that can change."
'Significant movement needed'
An EU summit is due to take place on 19-20 October, when leaders of the remaining 27 member states will discuss the status of the Brexit talks.
The UK has wanted talks on the terms of its departure to take place in tandem with discussions on trade.
The EU has rejected that proposal, saying no new trade agreement can be finalised until the UK has withdrawn from the bloc.
Under an agreed schedule, progress must be made on citizens' rights and financial issues before the talks can move on to future arrangements.
Mr Coveney said the EU was unlikely to agree to move to the second phase of the negotiations "unless there is a significant further move from the British government".
Prime Minister Theresa May is due to make a major Brexit speech in Italy next week, in which she will outline the UK's wish for a "special partnership" with the EU after Brexit.
Mr Varadkar has suggested that more clarity is required from the UK on the future status of the Irish border, which will be the UK's only land frontier with the EU.