Most supplies for US-led and Nato forces in Afghanistan are sent through Pakistan, but convoys have repeatedly come under attack from pro-Taliban fighters in the border regions.
A US source confirmed that the deal was expected to go ahead and said it would make a step forward in co-operation over Afghanistan.
Dmitry Medvedev, the Russian president, has repeatedly said he is ready to work with US-led forces and the Nato military alliance in Afghanistan, although Moscow has ruled out sending any of its own troops to fight in the country.
"America respects Russia, we want to build relations where we deal as equals"
"The Russians have always been interested in helping their American friends in Afghanistan and now is the right time," Alexander Pikayev of the Institute for World Economy and International Relations told Al Jazeera.
"Moscow, after last year's differences around Georgia, is really keen to improve relations with the United States," he said.
Obama is due to arrive in Moscow on Monday for a highly anticipated visit during which Afghanistan is expected to be just one area of discussion.
Talks are also likely to focus of US plans to build a missile shield in eastern Europe and nuclear disarmament as the two nations seek to mend ties.
On Saturday, Obama had warm words for his Russian counterpart after voicing some sharp criticism of the attitude of Vladimir Putin, his predecessor, two days earlier.
"America respects Russia, we want to build relations where we deal as equals," he told the Vesti Russian-language news channel on Saturday.'Forward-looking'
He said Medvedev was a "thoughtful, forward-looking individual" who is "doing a fine job of leading Russia into the 21st century".
Obama went on to describe Putin as being "a very strong leader for the Russian people".
Medvedev also spoke positively of the chances for success in a statement released to mark US independence day.
"We expect that concrete results will be reached at the summit which will open up new prospects for the development of our relations," he said.
"I sincerely hope that with our mutual efforts ... Russia-US relations can be brought to a new level of quality."