Kerry and Lavrov are expected to discuss in detail the possibility of the first U.S.-Russian agreement to share intelligence and targeting data for airstrikes over the battle in Syria, something Carter has largely opposed.
The Pentagon wants some assurances the Russians will live up to the terms of any agreement in which the U.S. makes concessions. Defense officials told CNN that, internally, Carter has expressed skepticism the Russians can be trusted.
State Department spokesman John Kirby on Monday would not publicly acknowledge Kerry and Lavrov are discussing a potential agreement, saying only, "Syria will be front and center; there's no question about that."
He added, "I can assure you that one of the key topics the secretary is going to want to cover with Russian officials is reduction in violence."
Washington is leading a coalition in fighting ISIS, which has taken advantage of the Syrian civil war to seize a foothold in the country. Moscow has also been engaged in military action, which it describes as aimed at driving out terror groups including ISIS but which the U.S. says has often been directed at American-supported forces opposing Syrian President Bashar Al-Assad. Assad is a key Kremlin ally, while the U.S. has called on him to leave office.
The U.S. wants "Russia to use the influence that we know it has on the Assad regime to get the situation in better control," Kirby said.
To that end, U.S. officials are beginning to sketch out what a possible agreement could look like. The Russians would gain a critical win they have been seeking for months: intelligence about where U.S. aircraft are operating.
The idea is the two sides would share what they know about targets involving both ISIS and al-Nusra, the al-Qaeda-affiliated group in Syria. Al-Nusra has gained strength recently and is considered one of the more capable groups fighting the Assad regime in some northeastern parts of Syria.
The challenge in northeastern Syria is that the U.S. has been unable to strike al-Nusra because they are intermixed with some moderate opposition elements America supports.
Another portion of a potential agreement with Russia could call for the Syrian air force to be grounded, a major U.S. interest, although it's acknowledged that their ground units would still go after the moderate opposition and even potentially civilians.
U.S. officials said, though, that a cooperative agreement with Russia could lessen the pressure the U.S. has been putting on the Russians to get Assad out of office. That is another key win for Moscow.
The U.S. still wants to see Assad encouraged to leave, although U.S. officials can't really say how that is more than a hope.
There is a growing sense in Washington that al-Nusra must be dealt with in Syria. One reason: If the U.S.-backed rebels can push ISIS out of their Syrian stronghold in Raqqa, there is concern al-Nusra could rapidly move into some vacuum there.
But from the Pentagon point of view, an agreement with the Russian military may be viewed as a loss. Defense officials have made it privately known that Carter is very skeptical the Russians would live up to their promises. And officials say the Pentagon still would not want to share the most sensitive information with Moscow.
Last month Carter publicly spoke about his concerns, using another name for ISIS.
"The Russians got off on the wrong foot in Syria. They said they were coming in to fight ISIL," he said. "And that they would assist the political transition in Syria towards a post-Assad government that could run the country and put that terribly broken country back together and give the people the future they deserve."
He concluded, "They haven't done either of those things."
Carter said an existing agreement with the Russians on air safety procedures over Syria will continue. But beyond that, he remains publicly cautious when asked about additional sharing of airstrike information.
"If the Russians would do the right thing in Syria, and that's an important condition, as in all cases with Russia, we're willing to work with them," he said. "That's what we've been urging them to do since they came in."