The pair met for lunch in Luxembourg ahead of a two-day European Council meeting in October in which Johnson wants to land a revised Brexit deal with the EU.
In a statement, the Commission said the UK had to bring forward suggestions that were compatible with the current withdrawal deal a Theresa May-era agreement that the UK's House of Commons, the lower legislative chamber rejected three times, Efe news reported.
"President Juncker underlined the Commission's continued willingness and openness to examine whether such proposals meet the objectives of the backstop," the Commission said.
"Such proposals have not yet been made," the Commission said, adding that it will remain available to work 24/7.
The Irish backstop is a mechanism that could temporarily keep the UK in a form of the customs union after Brexit to avoid a hard border between the Republic of Ireland and Northern Ireland if London and Brussels fail to agree on their future relationship.
"The October European Council will be an important milestone in the process. The EU27 remain united," said the Commission.
Speaking to reporters in Luxembourg, Juncker said the encounter with Johnson was a "friendly meeting" and that negotiations will continue at "high speed". The UK is on track to leave the EU on October 31.
Johnson embarked on a last-minute bid to secure changes to the current withdrawal bill, which he opposes, largely over the terms and conditions of the Irish backstop. But the EU has been reluctant to change the contents of the withdrawal deal.
The Council meeting is due to take place over October 17-18.
Johnson, who leads the Conservative Party, has lost control of the Brexit process in the Commons, where opposition parties have banded together to take over the agenda. He has also lost his working majority.
Last week, MPs passed a law that would require him to request an extension to the negotiation process rather than take the UK out without a deal.
( With inputs from IANS )