The chain said families could safely sit together, away from strangers, to watch movies.
Screening times would be staggered, and there would also be enhanced cleaning.
The government has said some hospitality businesses like cinemas could reopen from 4 July - depending on how the pandemic progresses.
"We have been liaising closely with authorities across Europe to design operating procedures that can provide the degree of social distancing required and allow an experience for our customers and staff that is as safe as possible," Vue said.
The company said measures could include "physically isolating family groups through our online booking systems, staggering film times to maintain social distancing and operate responsibly, and introducing enhanced cleaning and employee protection protocols".
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Vue - one of the biggest UK cinema chains - added that "big screen entertainment is a force for good in society", and would provide "an accessible and controlled way for families to begin to enjoy life outside their homes".
Earlier this month, chief executive Tim Richards told the BBC he hoped to have the chain up and running in time for the launch of director Christopher Nolan's action movie Tenet on 17 July.
"We can control how many people come into our cinemas," he noted.
UK cinemas shut in mid-March. The boss of the UK Cinema Association told the BBC "most venues" would be ready to reopen by the end of June, as long as safeguards were in place.
Phil Clapp said he welcomed the proposed July restart, while recognising "there are a host of wider public health considerations which mean that may not be possible, and we will of course respond accordingly".
He said: "We remain in discussion with the government on the exact nature of the safeguards that will be required, some of which have been touched upon by Vue in their response, but all of which will be observed by the entire cinema sector to offer every reassurance to audiences and staff around their continued safety."
Step three of the government's new coronavirus conditional plan would potentially see leisure facilities like cinemas reopen, along with food service providers, pubs, hotels and places of worship - but only if they meet the Covid-19 Secure guidelines.
Buildings that are more likely to attract crowds, like gig venues and theatres, will not be allowed to properly reopen at this suggested earliest stage.
Last week, Cambridge University virologist Dr Chris Smith questioned the validity of reopening any such venues, from both a medical and economic standpoint, until a vaccine emerges.