Macron made the statement during a phone call with Macron on the weekend, during which the latter also spoke to several other EU leaders, the BBC reported on Monday.
A French government official said President Macron told Johnson "that the negotiations should continue swiftly with (UK Brexit negotiator) Michel Barnier's team in coming days, in order to evaluate at the end of the week whether a deal is possible that respects EU principles".
But Johnson said the EU should not be "lured" into thinking there will be a delay to Brexit beyond October 31.
But under the Benn Act, passed last month, the Prime Minister must write to the EU requesting a Brexit extension if no deal is signed off by Parliament by October 19, unless MPs agree to a no-deal Brexit.
The Prime Minister told President Macron that he believed a deal could be achieved, but that the EU must match compromises made by the UK.
The comments come ahead of a key few days of negotiations as both parties try to find a new agreement in time for a summit of European leaders on October 17 and 18.
Arrangements for preventing a hard border on the island of Ireland continue to be a sticking point, with the EU calling for "fundamental changes" to the UK's latest proposals.
A senior Downing Street source said: "The UK has made a big, important offer but it's time for the Commission to show a willingness to compromise too. If not the UK will leave with no deal."
Government papers submitted to a Scottish court said that Johnson will comply, despite his assertion that there will be "no more dither or delay", the BBC reported.
The source called Benn Act a "surrender act" and said its authors were "undermining negotiations".
"If EU leaders are betting that it will prevent no deal, that would be a historic misunderstanding," they said.
Speaking to the BBC, Brexit Secretary Stephen Barclay said on Sunday that talks were underway with Labour and other opposition MPs aimed at securing their support for a new deal.
He said ministers were "considering" the idea of putting the Prime Minister's proposals to a vote in Parliament to test support for them ahead of the EU summit.
Meanwhile, Labour leader Jeremy Corbyn is set to meet the leaders of other opposition parties, the Scottish National Party, Liberal Democrats, Greens and others on Monday to decide the next steps to "hold the government to account".
( With inputs from IANS )