He was speaking as EU 27 leaders arrived for European Council Brexit talks on Thursday morning.
Leo Varadakar, Angela Merkel, Giuseppe Conte and European Council president Donald Tusk were among the first to arrivef for the Brussels summit, wtih Theresa May admitting to reporters that an extension to the Brexit transition period was possible.
Mr Tajani said: “There are three key points. The rights of EU citizens living in the UK, and in Europe, money and the third point is the back stop.
“We need to work on this, we do not have agreement, but I want to be optimistic.
European Parliament president Antonio Tajani says EU wants three-year Brexit transition period
“Without that third point it is impossible for us to vote in favour for the agreement.”
When asked about Mrs May’s stand on a Brexit implementation period extension he said: “Yesterday she spoke on the transition period but not in favour or against.
“The proposal is on the table.”
The European Parliament would support a three-year implementation period, Mr Tajani added.
When asked about EU chief negotiator Michel Barnier’s speech Mr Tajani said: “Michel Barnier’s speech was more flexible but on the content there was no news.
“We need to work hard to achieve the goal step by step.”
The EU was “committed” to the backstop solution for Northern Ireland, which was “a key point” of the Brexit negotiations, he added.
Mr Tajani said:“Without that, the Parliament will not be able to vote in favour of the agreement.
“We want a flexible border. But we also want to protect our health and our industry.
“The Parliament is also favourable to the idea of a third year for the transition period.”
Proposals over the Nothern Ireland backstop are the major sticking point of the Brexit negotiations, with the DUP – currently propping up Mrs May’s government – threatening to vote against the Budget if they are unhappy with the final plan.
The deal could see the province remain under EU customs rules, although Mrs May has said she would not allow a deal that treats Nothern Ireland differently from the rest of the UK.
Theresa May tells reporters a Brexit implementation period extension has been discussed
After meeting with Irish Taoiseach Leo Varadkar on Thursday morning, Mr Tajani revealed he could travel to Ireland to show EU solidarity with Dublin.
Mr Tajani said: ”I may visit Ireland to explain Parliament’s position which is in full support of the Republic of Ireland.”
The Northern Ireland border needs to be flexible to protect peace and the Good Friday Agreement, Mr Tajani added.
Meanwhile, Mrs May admitted that an extension period to Brexit is on the negotiating table.
Mr Tajani has said he may visit Ireland in bid to resolve border Brexit impasse
Mrs May told reporters a transition period could stay open for a few months more than planned, but is adamant the implementation period must last only until the end of December 2020.
Mrs May said: “A further idea that has emerged – and it is an idea at this stage – is to create an option to extend the implementation period for a matter of months – and it would only be for a matter of months.
“But the point is that this is not expected to be used, because we are working to ensure that we have that future relationship in place by the end of December 2020.
“I’m clear that it is possible to do that and that is what we are working for, and in those circumstances there would be no need for any proposal of this sort and I’m clear that I expect the implementation period to end at the end of December 2020.”
She said the option of an extension to the transition between the end of 2020 and the start of any future relationship with the EU had been suggested.
Theresa May arrives for EU 27 summit and tells reporters she wants UK to leave EU by December 2020
Mrs May also shot down EU plans to resolve the Northern Ireland border impasse as the EU and Britain tries to overcome the hurdle and reach a withdrawal agreement.
Brussels original plan over a backstop to solve the border problem “is one we could not accept”, the prime minister said.
Mrs May added: “Just to remind everybody, the backstop is what would come in place to ensure that there would be no hard border between Northern Ireland and Ireland if the future relationship is not in place by the end of the implementation period.
“Now, the original proposal from the EU is one that we could not accept in the UK. It would have created a customs border down the Irish Sea. Earlier in the year we put forward a proposal as to how to deal with this issue.
“It would have created a customs border down the Irish Sea. Earlier in the year we put forward a proposal as to how to deal with this issue.”