Rotheram said fewer people may dump prohibited materials such as asbestos at household waste sites if it was less of “an easy option”.
However, he said fly-tipping and low recycling levels remain a major concern across the city region.
“I’ve got no intentions at all of supporting something that makes it more difficult for people to recycle,” he said.
“Some people, as you know, don’t recycle.
“It’s the law of unintended consequences. If people go and say, ‘the tip’s closed’, they lash it in the first available space, so we don’t want to indirectly create problems for ourselves.”
MRWA is contracted by the Liverpool City Region Combined Authority to operate the region’s household waste recycling centres until 2029.
It said the consultation was aimed at boosting recycling rates and ensuring the service continued to meet the needs of households in the years ahead.
Rotheram added: “We’ve got really, really poor levels of recycling at the moment and it’s going in the wrong direction, so we need to do something about that as a thing in itself.
“Every single option you have got to look at.”
Residents are being asked to share their views before the consultation closes on 22 September.