Fully vaccinated adults could avoid quarantining if pinged by the NHS app by taking Covid tests for five days instead.
Vaccines minister Nadhim Zahawi said the current system of people going into 10 days of isolation despite having both inoculation doses is being reviewed.
He said the app - which sees people check into venues so they can be notified if anyone else there later tests positive -"was developed and operationalised at a time when we didn't have vaccines".
It comes as statistics expert Professor Sir David Spiegelhalter said life is likely to be "massively disrupted" over the summer as cases continue to rise.
He said it would make sense to get the rules "in proportion", as Mr Zahawi confirmed the Government was looking at ways to tweak the app.
Speaking on Trevor Phillips On Sunday on Sky News, the minister said: "The team are looking at how we use that app in terms of alerting people to those around them who test positive."
He added: "It's important to look at that in a new context of this massive vaccination programme and make sure that it is fit for purpose for this new world including, for example, being able to take maybe five days, as we have piloted, of lateral flow tests and upload them to the system rather than having to self-isolate."
There have been concerns that people are deleting or disabling the app amid a huge rise in exposure alerts sent to users in England telling them to isolate.
Representative body NHS Providers said a growing number of trusts had told them of their concerns in recent days about how self-isolation of staff is now "significantly impacting their ability to deliver care".
Downing Street said on Friday that ahead of Step 4 of restrictions being lifted, expected on July 19, officials were examining whether NHS staff could be freed of the obligation to self-isolate if "pinged" by the Covid app.
Under current plans, people who are fully vaccinated will be able to forgo self-isolation even if the app detects they have been in contact with someone who has tested positive after August 16.
Hospitality chiefs have warned that the delay between restrictions being lifted and self-isolation rules being eased risks "the summer being cancelled and vast swathes of the population unnecessarily confined to their homes".
Sir David, from the University of Cambridge, said if people are vaccinated and then pinged by the app, it is a "very low percentage" who have "actually got the virus".
He told BBC One's The Andrew Marr Show: "Few people told to self-isolate actually have an infection, and especially if they're vaxxed, and so I do think it makes sense to get this in proportion to actually 'what are the benefits of this massive disruption?"'
Asked about stories of people deleting or disabling the app to avoid being "pinged" and told to self-isolate, he said: "I'm not going to comment on whether I think that's a good or bad thing to do."
Sir David said it is "absolutely inevitable" there will be a "big wave" of coronavirus cases as restrictions are lifted.
Health Secretary Sajid Javid has already said case numbers could reach 100,000 per day in the summer as measures are eased, and Sir David said he thinks this is "quite possible", adding that relaxing "everything at once on July 19 will only make that more likely".
The UK's national statistician Professor Sir Ian Diamond said the experts are "keeping an absolutely close, minute-by-minute eye" on the number of Covid-19 infections, and that in terms of antibody levels, the UK is doing "very well".
Also speaking to Sky, he said the link between infections and being admitted to hospital, having serious disease and dying has been "severely weakened".
