EU leaders yesterday offered to help Labour unpick Boris Johnson's Brexit deal.
Irish premier Simon Harris said his country would help 'facilitate' a closer deal with the UK 'every way we can around any European table'.
Mr Harris said there was a 'willingness to have those conversations' in Brussels about a new deal, which could include a form of free movement for young people.
Germany said it was working with Labour 'to see how the UK can move closer to the EU'.
Sir Keir Starmer, meanwhile, said work had 'already begun' on negotiating changes to the 'botched' Brexit deal.
Irish premier Simon Harris said his country would help 'facilitate' a closer deal with the UK 'every way we can around any European table
The Prime Minister told reporters in Edinburgh: 'We intend to improve our relationship with the EU and that means closer trading ties with the EU.'
He added: 'I do think that we can get a much better deal than the botched deal that Boris Johnson saddled the UK with.'
Discussions could be held this week when Sir Keir meets EU leaders in the margins of the Nato summit in Washington.
They are likely to be accelerated when he hosts a summit of European leaders later this month.
Business Secretary Jonathan Reynolds welcomed the 'constructive attitude' of EU leaders.
He said Labour was right to 'explore' closer trade ties, but insisted the Government would not 'revisit constitutional arguments' about Britain's membership of the EU.
Sir Keir Starmer said work had 'already begun' on negotiating changes to the 'botched' Brexit deal
Mr Johnson yesterday warned that Labour was beginning a 'great sell out' of the British public over Brexit.
'Behind these harmless sounding agreements is the reality that the UK will be accepting rules set by Brussels – no matter how onerous – with no UK say on the making of those rules,' he told The Mail on Sunday.
Mr Johnson warned that Britain is 'on the road to serfdom' under Labour plans to cosy up to the EU – quoting 20th-century economic philosopher Friedrich Hayek.
Mr Hayek, whose work inspired Margaret Thatcher, warned that centralised planning – such as the EU – could lead to totalitarianism.
Mr Johnson yesterday warned that Labour was beginning a 'great sell out' of the British public over Brexit
The Nobel-Prize winner believed only free markets could protect individual freedoms.
Last night, David Lammy – who visited Poland yesterday – said Labour is seeking an joint declaration with the EU to usher in a security pact covering defence, energy, climate change, pandemics and illegal migration.
The Foreign Secretary has also accepted an invitation to the September meeting of the EU foreign affairs council – something rejected by the previous Conservative government.