County council bosses say tips in Lichfield and Burntwood will be reopened “when the time is right”.
The household waste recycling centres were shut as part of social distancing measures introduced because of the coronavirus outbreak.
But Labour councillors have called for them to be reopened to prevent an increase in fly-tipping.
And Secretary of State Robert Jenrick said he had asked councils to prepare for the gates to be unlocked at sites across the country.
Cllr Mark Deaville, Staffordshire County Council’s cabinet member for commercial, said the centres had been closed in line with official guidelines – and that trips to the tip were not classed as essential journeys:
“Government guidance has been clear that people should only leave their homes for essential travel, such as for exercise, food shopping, or work, and visiting a recycling centre does not fall into that category.
“Since the Government announcement to stay at home, closure has protected workers at the recycling centres and the public using them and reduced the pressure on the NHS. It’s also allowed those workers to support essential services elsewhere in the authority.
“We are monitoring the situation and are keeping in touch with the Government and neighbouring local authorities.
“When the time is right it is very likely that we will reopen the sites with social distancing rules in place and we will publicise all those arrangements beforehand.”Cllr Mark Deaville, Staffordshire County Council