"The political realities have changed since Mr Barnier's instructions were set," Barclay wrote.
"Since the last mandate was agreed, 61 percent of all the EU states' MEPs have changed. Such a fundamental shift illustrates the need for a change of approach.
"Mr 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." Former prime minister Theresa May quit after delaying Brexit
twice while she tried unsuccessfully to get the divorce terms she struck with Brussels through the British parliament.
But the EU has refused to reopen the deal, the result of 17 months of tough negotiations.
Johnson has ramped up preparations for leaving without any agreement.
However, some British lawmakers have vowed to stop him, fearing the economic consequences of severing ties with Britain's closest trading partner overnight.