Writing in the Mail on Sunday, Brexit Secretary Stephen Barclay said "political realities" had changed after the European Parliament elections that were held in May, reports the BBC.
New MEPs were elected in 61 per seats of seats, he said, marking a "fundamental shift".
He called on EU leaders to allow Barnier to negotiate in a way that finds "common ground" with the UK.
Brussels has consistently insisted that the withdrawal agreement - one of two main elements of former Prime Minister Theresa May's Brexit deal, which was resoundingly rejected by MPs - cannot be renegotiated.
Barclay said Barnier had told him in their discussion last week that he is bound by the instructions given to him by the European Commission and leaders of member states.
But the change in the EU Parliament means there is a need for the EU to alter its approach, the Secretary added.
"Barnier needs to urge EU leaders to consider this if they too want an agreement, to enable him to negotiate in a way that finds common ground with the UK. Otherwise, no deal is coming down the tracks," he wrote in the Mail newspaper.
Barclay added that the former Foreign Secretary Boris Johnson's appointment as Prime Minister last month only strengthened the UK's mandate to leave on October 31, the BBC reported.
Johnson has ramped up his rhetoric over his desire to take the UK out of the EU by October 31, as part of his "do or die" commitment.
He has clashed with EU leaders over his demands to remove the Irish backstop - which prevents a hard border if the UK and EU fail to agree a long-term trade deal - from the withdrawal agreement.
( With inputs from IANS )