NATO is struggling to come up with more troops, with some European members reluctant to send their forces to southern and eastern Afghanistan where U.S., British, Canadian and Dutch soldiers clash almost daily with Taliban militants.
Canada, with 2,500 troops in southern Afghanistan, wants NATO allies to provide another 1,000 soldiers to reinforce its combat forces as a condition for keeping its troops in the country.
The senior U.S. administration official said Karzai and Cheney would also discuss steps the Afghan government needs to take on fighting corruption and narcotics.
The Afghan government promised a major crackdown on corruption this week, admitting it was rampant in every level of the state. Afghanistan is ranked 172 out of 180 countries on Transparency International's corruption perception index.
The country's raging illicit opium industry is the main factor driving corruption, with the illegal crop accounting for as much as a third of the entire economy. Afghanistan last year produced 93 percent of the world's opium, which is processed to make heroin, and efforts to curb the crop have largely failed.
Karzai and Cheney are also expected to talk about Afghan parliamentary and presidential elections next year and discuss Pakistan in the wake of elections there and how the neighbours can work together to fight the common Taliban threat, the administration official said.
Cheney will also meet U.S. troops in Afghanistan.
(Writing by Jon Hemming; Editing by Alex Richardson)