The government has imposed a lockdown on the city of Leicester, which has a higher infection rate than anywhere else in the country, in its first major attempt to curb an outbreak with local rather than national measures.
Speaking before Monday's decision, which could see Leicester play their three remaining Premier League home games at neutral venues, Rodgers said his team had to be flexible.
"Nothing has changed in terms of how we have been working thus far throughout this situation," Rodgers told reporters. "It's a very safe environment for the games to be in. We will just keep working until we are told otherwise.
"I have always said we will react accordingly. We have to have agility in this period. I think in this moment in time we are in the safest place we can be in terms of our work, the stadium also."
Leicester visit Everton on Wednesday and are then set to host Crystal Palace on Saturday. Palace manager Roy Hodgson said he would follow the league's guidelines on where his team have to play that fixture.
"We're happy to go up and play Leicester wherever the Premier League feels we should play... I'm perfectly happy to let the Premier League take care of that," said Hodgson. (Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Peter Rutherford )