He said negotiators "now largely have common draft treaty texts" but said "significant elements are of course not yet agreed".
He faced down the ultimatum from Mr Coveney, who told Ridge that, if that happened: "This is a deal that won't be ratified by the European Union".
London has acknowledged the bill could violate worldwide law by over-riding the divorce agreement it previously agreed with the EU.
"If the British government is determined to continue with their Internal Market Bill, to reintroduce parts of that bill that were removed by the House of Lords this week, then I think this is a deal that won't be ratified by the EU", Mr Coveney said on Sophy Ridge on Sunday on Sky News.
The head of the government legal department resigned, as did a Tory minister, and past Conservative prime ministers and leaders - including Brexiteer Michael Howard - have opposed the bill, while Brussels has started legal action.
Speaking on the same program, Irish Foreign Affairs Minister Simon Coveney said negotiators were running out of time, and "this is move week".
"People have persevered with these talks".More news: China's sweeping COVID controls put frozen food importers on ice
Mr Coveney also highlighted the risk that a deal could collapse over fisheries, saying a compromise both sides could live with was needed.
As he returned to returned to Brussels for another week of talks, the U.K.'s chief negotiator, David Frost, said he "will not be changing" his position in discussions with his European Union counterpart.
United Kingdom chief negotiator David Frost is in Brussels for another round of negotiations ahead of a European Council video summit on Thursday which has been touted as a deadline for a draft deal.
Meanwhile, ministers will today tell Irish businesses to prepare for the increased customs regulations that will come into effect from January, even in the event of a last-gasp deal on the UK's future relationship with Europe.
"You can always squeeze out extra time if you need to, if you're almost there".
"Otherwise, it gets quite hard and we do start to run out of time to implement it".
On Friday, Johnson's senior aide Dominic Cummings - one of the architects of the "leave" victory in the 2016 Brexit referendum - was sacked, amid faction fighting in Number 10, but there has been no sign this will change the direction of trade talks.More news: Lahore Qalandars vs Multan Sultans
United Kingdom sources said there were still "quite big gaps" between the sides.
© AP Britain's prime Minister Boris Johnson walks past the "Field of Remembrance" as he leaves Westminster Abbey after Armistice Day service in London, Wednesday, Nov. 11, 2020.
"We are more likely to get a deal than not, purely because the consequences of not getting a deal are so significant and so costly for the United Kingdom and Ireland as it happens, and for some other European Union countries", Coveney told an online conference.
"We have got to make big progress this week", Mr Coveney told Sky News yesterday.
"If we can't agree by then, then I do not see that there will be a free trade agreement between us, and we should both accept that and move on". Because Britain is leaving the single market and customs union, United Kingdom businesses will face new border checks and controls whether or not an agreement is signed. Without one, millions of consumers will face the return of quotas and tariffs for the first time in a generation.
The National Audit Office warned last week that the government had not done enough to prepare for 31 December and that there would be disruption at the border on 1 January no matter what.More news: Ontario reports 1,248 new cases of COVID-19, 20 deaths in LTC