Islam Times reports from Press TV: "Whether there would be some US troops continuing to stay after 2014 depends on the strategic declaration between the two countries or the precise document we are discussing," said Karzai, who is in Pakistan's capital Islamabad where he is on the second day of an official visit.
He added that more discussions would be held on the issue in the future.
US-led foreign forces will be pulled out of Afghanistan in 2014. The date was agreed on during a NATO summit last year.
Now, Karzai says Kabul and Washington have exchanged proposals on possible US presence in Afghanistan beyond 2014.
"Our proposal had gone to the US government in response to their proposal. A delegation will come from the United States to discuss this and that will determine the nature of US presence in Afghanistan (after 2014)."
According to official figures, at least 2,518 US-led soldiers have been killed in Afghanistan since the US-led invasion began in 2001.
Senior US and NATO officials have signaled that foreign troops will remain in the country beyond 2014.
This is while US President Barack Obama had pledged a major drawdown from Afghanistan by July 2011.
Experts have described the new contradictory transition dates as a devastating truth for Americans.
Washington says the transition does not mean that Afghan forces will be in charge everywhere. Obama has promised to keep American forces in Afghanistan even after other Western countries withdraw their troops.
Thousands of Afghans have so far been killed during ground and aerial operations by foreign troops.