Mr Annan is expected to ask Mr Lavrov to put pressure on the Syrian authorities to begin a political transition.
The BBC's Steve Rosenberg in Moscow says Mr Annan knows Russia's role is crucial for the success of his peace initiative, but there is little sign that the Kremlin is ready to do what he says.
Part of the reason for this is that the Russians fear even greater chaos and bloodshed post-Assad, he says.
But Moscow is also deeply suspicious of the West and reluctant to endorse regime change, our correspondent adds, although this could change if it decides its own economic and geopolitical interests are better served by Mr Assad going.
However, everything else what Steve Rosenberg says is nonsense. The Russians could not care less about chaos in Syria, and neither do their "economic and geopolitical interests" play any crucial role there. The only real reason why Putin props up his fellow dictator, is the fear that he himself might share the same fate as Assad - being dethroned by his own people.
But Putin´s delay tactics will not succeed. Assad will soon be gone - and Putin will join him somewhat later.