The “Greeks-EU” trade deal would see Greek businesses allowed to sell their products across the bloc, but not to other EU members.
The agreement is not likely to get far in the European Parliament because it is tied up in negotiations with the Greek government.
But in the EU, it is a rallying cry for the hard left and the nationalist Greek party Golden Dawn.
Its main leader, Nikolaos Michaloliakos, is a former finance minister.
He is also a member of Greece’s ruling Syriza party, which has long called for an end to the EU’s austerity measures.
Ahead of the EU summit on Monday, Mr Michaloniakos said the deal would bring a “greater unity to the European Union and a fairer and more prosperous future for all its members”.
A senior Greek official told Reuters news agency the deal was still being drawn up and that Greece would not be able to open the borders with Greece or the EU until it is “done”.
“The Greek government is still negotiating with the EU but it is very early and we cannot say anything at this point,” he said.
“It is very hard to predict what the agreement will be and the details.”
Golden Dawn is a nationalist party with close links to Greece’s leftist-led government, which was defeated in the election in June and is now in opposition.
Its leader, Nikos Michals, who has been jailed for more than five years, said he would hold the Greek parliament’s approval until the deal is ready.
“We have to start a negotiation with the European Commission before we are ready to enter into this deal,” he told Reuters.
“But the Greek people will be the ones who decide this.”
The deal is likely to be seen as a victory for the Greek economy and its Prime Minister, Alexis Tsipras, who wants to bring Greece closer to the rest of Europe.
But its critics, including the opposition Labour party, say it is more likely to help the ruling Syrizas and to the extreme right of the party, whose leader, Antonis Samaras, is now being investigated over the murder of a leftist journalist in 2014.
A spokesman for the European parliament said Greece would have to wait until it signed up to the deal before it could start the trade pact.
European leaders agreed on Monday to extend a six-month extension of a bailout program to help Greece recover from the worst of the eurozone crisis.
It is the latest attempt by the EU to push through an agreement that will allow the Greek financial system to reopen.
Its leaders hope the agreement, expected to be approved in a vote on Tuesday, will enable Greece to get out of a debt crisis that has seen it default on its debts in two previous bailout agreements.