Speaking after meeting the DUP and other Northern Ireland parties, Leo Varadkar said he thought a deal can be done.
But he also said he would only be seeking to "restore confidence and trust" with Mrs May at the private dinner on Friday.
The prime minister had been hoping to make progress on the issue of the backstop, but Mr Varadkar made clear just hours before their meeting that he would be "sharing perspectives" rather than doing any negotiating.
The backstop - a customs plan to avoid a "hard" border between Ireland and Northern Ireland if a Brexit deal is not reached - remains the main stumbling block in Mrs May's plan to take the UK out of the European Union.
Mr Varadkar said any actual negotiations could only take place "between the European Union and the United Kingdom".
His comments came after Mrs May and her cabinet ministers had appeared to pin their hopes on the dinner, indicating it was a sign that a new solution could be reached, enabling her to get a deal through parliament.
Speaking in Belfast to political parties before meeting Mrs May, Mr Varadkar said: "I think everybody wants to avoid no-deal, everybody wants to avoid a hard border and everybody wants to continue to have a very close political and economic relationship between Britain and Ireland no matter want happens.
"There is much more that unites us than divides us and time is running short, and we need to get to an agreement really as soon as possible, and I'll be working very hard and redoubling my efforts, along with government, to do that."
Downing Street said Mrs May would be "emphasising what we are looking for, seeking the legally binding changes to the Withdrawal Agreement that parliament said it needs to approve the deal".
She was joined by her chief of staff Gavin Barwell and her chief Brexit negotiator Olly Robbins for the dinner at Farmleigh House.
Arlene Foster did not indicate whether she spoke to the taoiseach about alternatives to the backstop, and said it was pointless to discuss an extension to Article 50.
Article 50 is the section of the EU treaty which allows member states to leave, and triggering it gives a two-year period for a new deal to be reached. The UK's negotiation period is due to end on 29 March.
Attorney General Geoffrey Cox held talks in Dublin with his Irish counterpart Seamus Woulfe.
Mr Cox has been leading work on providing either a time limit to the backstop or giving the UK an exit mechanism from it.
Dublin has said the backstop cannot be time limited because it provides an "insurance policy" again the hard border on the island of Ireland.
But Mrs May wants legally binding assurances that the UK will not end up trapped in the EU via the backstop.
Stephen Barclay, the Brexit secretary, will have his first continental talks when he meets Michel Barnier, the EU's chief negotiator on Monday.
Elsewhere, Mrs May has been given a warning by senior Tories that the "monumental" problems with her Brexit plan cannot be solved by "cursory tweaks".
The ex-ministers - Remainer Nicky Morgan and Brexiteers Iain Duncan Smith and Owen Paterson - have been taking part in talks to find an alternative to the backstop following a Commons vote in favour of replacing the measure.
"The backstop in anything like its present form is simply never going to pass the Commons," they wrote in the Daily Telegraph.
"It is almost as if the Prime Minister has forgotten the scale of the original withdrawal agreement's defeat (by 230 votes) or how unacceptable the backstop proposals remain to significant numbers of MPs on both sides of the House."
Meanwhile, the Financial Times reported that trade talks with Japan on a post-Brexit deal had stalled.
The newspaper said Tokyo has agreed to extend the existing terms for the duration of a transition period if the UK strikes a deal with Brussels - but in a no-deal Brexit UK-Japan trade would be on World Trade Organisation rules.
A Department for International Trade spokesman said: "Our priority is to avoid disruption to businesses as we leave the EU and more DIT staff have been allocated to no-deal planning.
"The Japanese Prime Minister and Theresa May agreed this January both countries would work quickly to establish a new economic partnership between Japan and the UK using the basis of the EPA (Environmental Protection Agency)."