"But, as we've said before, we continue to explore options, alternatives and proposals with respect to the fight against Nusra and Daesh in Syria ," he said.
"And... to the degree to which the Russian military is willing to be committed to the fight against those two groups, and exclusively those two groups, that's a conversation that we're willing to have," Kirby added.
"But there's no military coordination going on now." There was no word as to who Kerry will meet in Moscow on Thursday and Friday, but on previous such trips, he has met with Foreign Minister Sergei Lavrov before heading to the Kremlin to see President Vladimir Putin.
Russian forces are in Syria to support President Bashar al-Assad's regime in its five-year-old civil war against a variety of rebel forces, whereas a US-led coalition is focused on fighting the Islamic State group.
Washington has repeatedly urged Moscow to pressure its ally into agreeing on a ceasefire with so-called "moderate" guerrillas and to enter peace talks to end the civil war, but fierce fighting has continued.
Kerry's trip to Moscow come as part of a six-day, five-nation itinerary that will see him celebrate Bastille Day in France on July 14 before heading to Russia, Luxembourg and Belgium.
In London on July 18, he is slated to attend multilateral talks on the crises in Yemen and Syria but he will also be the first senior US official to visit after the new prime minister, Theresa May, is sworn in this week.