It is hoped using the sites as mass vaccination centres could help stop the spread of the Indian variant across the capital.
Wembley Stadium and Stamford Bridge - home of Chelsea FC - are said to be among the grounds being earmarked by officials.
The Indian strain is dominant in several parts of London, accounting for more than half of all positive test results in Brent - Wembley's borough - Hillingdon, Camden, Hounslow and Greenwich.
Under the government's national programme, those over 36 are currently eligible for a first dose.
NHS England has said any decision to allow anyone aged above 18 who would otherwise not be entitled to the jab right now would have to be rubber-stamped by Downing Street.
Stamford Bridge - the home of Chelsea FC - could also be used by health officials Credit: Alamy
It comes after Boris Johnson today vowed to take "very, very draconian action" to suppress alarming Covid mutations - but insisted the roadmap remains on track.
The PM tried to sooth fears on a visit to a vaccine centre in east London that June 21's freedom day is in peril over worries about the India variant.
Moving to ease concerns he said: "At the moment we see nothing conclusive that we have to deviate from the roadmap".
And he suggested a crunch data meeting in a few days time would tell us all more, urging the nation to hold tight.
He warned the nation to be cautious and vowed: "We're keeping everything under very close observation - we'll know a lot more in a few days' time.
"We're looking very carefully at the data, we're looking at the epidemiology. We're trying to work out what extent the Indian variant may be more transmissible."
Under fire from critics for dithering to ban travel with India, he stressed the government would come down hard to extinguish emerging strains.
The PM said: "We will continue to take very, very draconian action in respect of all variants coming from wherever around the world."
Last night Government advisers warned that some rules such as masks or social distancing are likely to stay after June, when the PM has previously said he hopes all rules will be able to be ripped up.
But fears over the new Indian variant of Covid, which is spreading much quicker in some communities, is causing ministers to urge extra caution.
The Indian Covid variant has been found in 40 per cent of local authorities in England with the B.1.617.2 strain is now dominant in 23 areas, data from the Sanger Institute revealed.
Health Secretary Matt Hancock said yesterday the variant is now the dominant virus in hotspots such as Bolton and Blackburn with Darwen.
Both Sefton and Bedford have been labelled as areas of concern, and figures show the variant accounts for eight in ten cases of hospital admissions.
This is also the case in Bolton, Blackburn, Chelmsford and Croydon.
Others parts of the country largely testing positive for the mutation include Nottingham, West Lancashire, Oadby and Wigston in Leicester, Stevenage, South Northamptonshire, Broxbourne, Bromley, Dartford, Sevenoaks, Canterbury, Rushmoor and Hart.
Boris Johnson says we 'see nothing conclusive' that suggests we have to 'deviate from roadmap' as he calls on Brits to get Covid jab