Juncker told Johnson on Thursday that the European Union would analyse any ideas put forward by Britain, provided they were compatible with the withdrawal agreement.
Johnson has repeated his pledge this week to renegotiate the withdrawal agreement and promised to take Britain out of the EU on Oct. 31 with or without a deal. He has also said the so-called Northern Irish backstop must be abolished to avoid a no-deal Brexit.
The backstop requires Britain to adopt some EU rules unless a future arrangement is found to keep open the land border between Northern Ireland and Ireland. The now-invisible frontier between the British province and EU member Ireland is Britain's only land border with the bloc.
Ireland's foreign minister said on Friday that Johnson's approach was "very unhelpful" and would block an agreement.
Concerns that Britain under Johnson is headed for a no-deal Brexit have sent sterling plummeting, although its moves this week have been minimal after investors rushed to price in a government under the eurosceptic face of the 2016 Brexit campaign in the run-up to his taking over.
"The Brexit impasse has already reared its ugly head, just days into Boris Johnson's tenure as UK prime minister ... The deadlock appears to solidify market concern over the prospects of a no-deal Brexit, keeping the pound rooted around the $1.24 mark against the US dollar," said Han Tan, analyst at FXTM.
Sterling fell 0.4% to $1.2406, a fair way below its weekly high of $1.2522. The pound hit a 27-month low of $1.2382 last week as fears of a no-deal Brexit jumped.
Banks say the pound could drop as low as $1.00 in the event of a sudden, disorderly exit from the EU, Britain's biggest trading partner.
Against the euro, the pound lost 0.2% to 89.695 pence per .
The Bank of England gives its monetary policy decision next Thursday.
Few economists expect the bank to change rates from the current 0.75%. The focus will be on policymakers' assessment of Britain's economic slowdown and whether it justifies a rate cut down the line.
Money markets are pricing in a 25-basis-point cut by June 2020.