"I think it is the desire of the people of countries that Indo-Pak matches should be restored soon," Ashraf, who recently undertook a week long visit of India, said.
The Pakistan Cricket Board chief said apart from the people even former players wanted to see the two countries play each other in bilateral series soon.
India froze bilateral cricket ties with Pakistan in 2008 after the Mumbai terror attacks.
But Ashraf, after his recent visit to India, has announced that both countries will soon be playing a bilateral match this year.
Sources in the board say that the PCB wants that both teams play two Twenty20 matches -- one in India and one in Pakistan at the Gaddafi stadium in Lahore -- in last week of December.
One source said India had agreed in principle to play one Twenty20 match in December in India.
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Ashraf said he was hoping for a major breakthrough and confirmation of dates for the one-off match when he met BCCI officials on the sidelines of the ICC meeting in Kuala Lumpur.
According to the source, the BCCI, in order to assist the PCB financially, has agreed to forgo broadcasting rights for the one-off match but details are still being worked out at the board level.