The use of vaccine passports could also be extended to lower divisions and other sports.
Talks are in an early phase with the Premier League to discuss whether supporters who have not been double-jabbed could be barred from entry, the PA news agency understands.
The use of vaccine passports could also be extended to lower divisions and other sports in England as ministers seek to reduce the surge of Covid-19 cases as other restrictions are ended.
While no final decisions have been made, it is currently being discussed whether vaccine passports could be introduced for seated events with a capacity of 20,000 people and over.
In unseated events such as music gigs, where there are greater concerns about strangers mingling and spreading Covid-19, the threshold for their introduction could be as low as 5,000 attendees.
A Government source said: “It’s important that fans can continue to watch sporting events over the autumn, which is why we’re exploring the role vaccines might play in this.
“This will not only allow full capacity stadiums but has the added bonus of incentivising people of all ages to go and get their jab.”
One area still said to be under discussion is whether a recent negative test could allow entry to football matches, but their use has been ruled out for nightclubs.