But the prime minister warned the cabinet there was still a "significant amount of work" to do, as EU and UK officials continue to hold talks, the BBC reported on Sunday.
Parliament will meet on Saturday and vote on any deal achieved by Johnson at a Brussels summit this week.
Labour said it would "wait and see" but would oppose anything "damaging".
The European Commission echoed the prime minister, saying: "A lot of work remains to be done."
Shadow business secretary Rebecca Long-Bailey told BBC One's Andrew Marr Show: "We don't think the Tories have moved too far on their deal."
SNP leader Nicola Sturgeon told the same programme: "We will not vote for the kind of deal specified by Boris Johnson."
Talks in Brussels between UK and EU officials - described as "intense technical discussions" - continued on Sunday and will re-start on Monday.
House of Commons Leader Jacob Rees-Mogg, a leading Brexiteer, told Sky News that "compromise" would be inevitable during negotiations.
He added: "I trust Boris Johnson to ensure the relationship the United Kingdom has with the European Union is one where we are not a vassal state."
Rees-Mogg also said he might have to "eat my words" and support a plan close to the one put forward by former Prime Minister Theresa May, which MPs rejected three times.
( With inputs from IANS )