Gilani, who was here on a five-day visit, told Sky News in an interview that he wanted to improve relations with the US following the killing of al-Qaeda chief Osama bin Laden in Pakistan last year.
"There have been lots of ups and downs in our relationship. We know the importance of the US. We really want to improve our relations. We are in the middle of discussions and I am sure that better things will come out," he said.
According to him, the relationship between the intelligence agencies of the two countries, the CIA and ISI, was "good".
He said: "All high-value targets of al-Qaeda - they have been achieved with the support and with the help of the ISI, with the CIA. Therefore, when we are working together so closely, I think there should be no hesitation in sharing information with Pakistan."
On the recent killing of British aid worker Khalil Dale in Pakistan, Gilani said: "He entered I don't know from which country, and his visa was expired. According to the laws and rules of my country, no foreigners can move without the permission of the interior ministry".
Gilani added: "I heard he entered from Iran, and he did not follow the advice of travelling to Baluchistan. We condemn this incident... We are sorry for the family. But at the same time, one should follow the rules within the country."
Gilani dismissed the political challenge posed by cricketer-turned-politician Imran Khan by saying that he was "a good cricketer" but "politics is another ball game".