Landrieu said she is not yet ready to announce anything but believes the Clean Air Act is not meant to be applied to carbon dioxide emissions.
She is a strong ally of oil-and-gas producers and refiners.
Murkowski could offer an amendment to debt legislation as soon as this week that would halt planned EPA rules to regulate emissions from sources like power plants and factories.
But she may also drop that plan, and instead seek a formal "resolution of disapproval" that would overturn EPA's recent "endangerment finding" that greenhouse gases threaten human welfare. The finding is a precursor to any EPA emissions rules.
Murkowski spokesman Robert Dillon said Murkowski will give a floor speech Thursday that reveals what approach she will take.