On Tuesday, the Premier League announced 18 positive cases from 1,479 tests carried out in the division, which is the most recorded since weekly testing started in May.
Manchester City’s game at Everton the day prior, had to be postponed following a number of positive cases in the visitors’ squad, making it the second Premier League game to be rescheduled this season.
Tottenham’s home game against Fulham on Wednesday is also in doubt after Scott Parker’s men reported a significant number of positive infections in their squad.
Allardyce has revealed West Brom, who were thumped 5-0 at home by Leeds United on Tuesday, have recorded one positive case in the past week, and wants the league to be halted.
"I'm very concerned for myself and football in general," Allardyce said. "Everyone's safety is more important than anything else.
"When I listen to the news that the variant virus transmits quicker than the original virus, we can only do the right thing, which is to have a circuit break [a tight set of restrictions designed to reverse the tide of the pandemic].
"I am 66 years old and the last thing I want to do is catch COVID-19.
"As much as we're getting tested – we had one positive this week – it seems to be creeping around. No matter how hard we try, no matter how many times we get tested, how we wear our masks, how we sanitise our hands, we're still catching a lot of infections around the country.
"If that helps [circuit breaker], let's do it and let the season run a little longer when we get through it."
