1043 GMT February 28, 2021
The measure was outlined in a four-part roadmap designed to bring the country out of its third coronavirus lockdown and back to normality, insidethegames.biz reported.
It has raised hopes fans will be able to attend events such as UEFA Euro 2020, Wimbledon and the Rugby League World Cup this year.
But the proposal is part of stage three of the roadmap and strict criteria must be met to move from stage to stage.
This includes the continued success of the vaccine rollout, a sufficient reduction in deaths and people needing hospital treatment, lower infection rates and no problems caused by new coronavirus variants.
The 10,000 fans rule covers large stadiums of at least 40,000 capacity.
Johnson has suggested that "normal life" could return in England by June 21 – the end of stage four when it is hoped all other restrictions will be lifted.
London's Wembley Stadium is due to host seven matches at the multi-city Euro 2020 this year, including both semifinals and the final.
The tournament, which was moved back a year due to coronavirus, is due to begin on June 11.
This means the third game at Wembley – England's final Group D match with the Czech Republic on June 22 – could potentially be held in front of a full house.
Wimbledon was the only one of the four tennis Grand Slams to be canceled entirely because of COVID-19 in 2020 and organizers reacted to the government's announcement with caution.
Play at the All England Club is scheduled to start on June 28 this year.
"We welcome the government's announcements and we look forward to continuing to work with them and the rest of sport with the ambition of welcoming spectators safely to our events this summer," a statement said.
"We remain focused on developing our plans within the scenarios of full, reduced and no public capacity so that we can remain as agile and flexible as possible to the government and public health situation.
England's staging of this year's Rugby World Cup is due to run between October 23 and November 27.
Other sporting events which could welcome fans include the conclusion to the Premier League football season, scheduled to end on May 23.
The British Grand Prix in Formula One is set for July 18 at Silverstone.