Foreign sides have stayed away since March 2009 when gunmen attacked the Sri Lankan team bus in Lahore, leaving six police officers and a van driver dead.
"I will be working closely with our international partners to ensure that the millions of cricket loving Pakistanis are not denied the ability to watch their stars and the game they love on our country's soil," Ashraf said in a statement issued by the Pakistan Cricket Board.
"For that I intend to work closely with ICC, ACC (Asian Cricket Council) and other boards in order to ensure a good relationship with them. This would also help in confidence-building for their decisions to come and play in Pakistan."
Since 2009, Pakistan has played most of its 'home' matches in the United Arab Emirates.
As for the team, Ashraf thinks allrounder Shahid Afridi still has plenty to offer as a one-day player after coming out of international retirement.
Afridi quit international cricket after differences with former PCB chairman Ijaz Butt and ex-coach Waqar Younis. However, he made himself available for selection after Ashraf took over from Butt earlier this month and Younis stepped down for personal reasons.
"As a Pakistan national and as a cricket viewer I think Afridi is very good one-day player," Ashraf told reporters, adding that he would meet Afridi soon to discuss the player's future.
"He has contacted me, but I could say something only after we both meet with each other."
Pakistan is currently playing a test series against Sri Lanka in the United Arab Emirates and it is likely Afridi's fate would be decided before the one-day series begins on Nov. 11 in Dubai.
Ashraf had talks with several PCB officials at its head office in Lahore on Friday and also plans to meet with various former test cricketers, including his favorite crickter-turned-politician Imran Khan.
"I want to develop consensus on how to move forward after meeting with legends," Ashraf said. "I am a very good listener."
Ashraf said he needed at least "two to three months" to settle down and study the working of the PCB.
For well over a decade, the PCB has been governed on an ad-hoc basis with the chairman appointed directly by the president of the country.
The International Cricket Council has set 2013 as the deadline for all the cricket boards to run their operations democratically.
Ashraf successfully headed Pakistan's top agricultural bank — Zarai Taraqiati Bank Limited (ZTBL) — for three years before being appointed as PCB chairman.