During a press conference in Brussels on Thursday, newly elected David Sassoli said that no new proposals had been received from the UK - and there would be no agreement without a Northern Ireland backstop.
The EP president said: "That is the position of European Commission, the position of the European institutions, in the European parliament and don't forget parliament will have the last word.
"Up to now I can say, and I would like to stress this point, the UK hasn't proposed any alternatives, anything that has been legally credible and workable.
"We are willing to go back to the original EU proposal, this is a significant point. We are willing to go back to the original proposal that the backstop will only be for Northern Ireland.”
Mr Sassoli said an extension beyond October 31 would be considered "provided it's something done for overriding reasons", such as a general election in the UK.
Mr Sassoli continued: "If there is a no-deal departure, that will be entirely the responsibility of the UK.
"The agreement negotiated is the best possible agreement as far as we're concerned...they protect the rights and life choices of British and European citizens."
Mr Johnson’s Government suffered a blow on Wednesday when judges at Scotland’s highest court ruled his prorogation of Parliament was “unlawful”.
Ministers have been protesting outside Parliament as opposition leaders called for an immediate recall of MPs.
Ahead of the conference, Mr Johnson downplayed the effects of a no-deal Brexit following the release of redacted parts of the Yellowhammer document.
Mr Johnson said: "It is very important to understand what this document is: this is a worst-case scenario which civil servants obviously have to prepare for, but in the last few months, and particularly in the 50 days since I've been Prime Minister, we've been massively accelerating our preparations.
"We're trying to get a deal and I'm very hopeful that we will get a deal with our European friends on October 17th or 18th or thereabouts.
"But if we have to come out on October 31st with no-deal we will be ready and the ports will be ready and the farming communities will be ready, and all the industries that matter will be ready for a no-deal Brexit.
"What you're looking at here is just the sensible preparations - the worst-case scenario - that you'd expect any government to do.
"In reality, we will certainly be ready for a no deal Brexit if we have to do it and I stress again that's not where we intend to end up."