A deal will need to be reached in mid-November to allow time to ratify it but talks have stalled in recent months, with the two sides struggling to reach agreement on at least two main sticking points.
The chief negotiators – Michel Barnier for the EU and David Frost for the UK – will resume talks in London this week.
On his arrival in London on Sunday, Barnier said he was “very happy to be back” and “the work continues” to secure an agreement.
Speaking ahead of the talks, Mr Johnson said: “I have always been very enthusiastic about a trade deal with our European friends and partners.
“I think it’s there to be done, the outlines are pretty clear. We just have to go on and do it if we can. And I told (the President of the European Commission) Ursula Von der Leyen yesterday. And she totally agrees with me. ”
The main obstacles to an agreement are the guarantees of fair competition, in particular as regards the rules on state aid; and fishing, a symbolic sector for Brexit supporters.
The move comes after Mr Johnson and EU chief Ursula von der Leyen spoke by phone on Saturday for “a review” of the progress of stop-start negotiations, both acknowledging that “significant differences” remain.
Another source of conflict between the two sides is Mr Johnson’s determination to push forward a controversial bill, despite warnings from US President-elect Joe Biden.
The Home Market Bill, due to be voted on by peers this week, would replace clauses in the Withdrawal Agreement that affect Northern Ireland.
The government has already admitted that it is breaking international law.
Mr Biden, who has Irish heritage, said in September that the Good Friday deal should not be “a victim of Brexit”, adding that a trade deal between the UK and the US would depend on maintenance of the agreement.
Mr Johnson said: “The purpose of this bill, and indeed the finance bill, is to protect and enforce the Good Friday Agreement and the Northern Ireland Peace Process.
“And again, this is one of the things that we are united on with our friends in the White House. ”
Labor leader Sir Keir Starmer wrote in The Guardian: “If the government is serious about resetting its relations with the United States, then it should take a quick first step and drop these proposals. “