The Pakistan Cricket Board (PCB) predicts international cricket will return to the country in 2012.
Pakistan have played all their matches overseas since the terrorists attacked the Sri Lanka team in Lahore in 2009.
But PCB chairman Zaka Ashraf has invited Bangladesh to tour, and said: "I am confident that international cricket will be revived in Pakistan."
The United Arab Emirates will host Pakistan's home series against England in the new year.
England will play three Tests, four one-day internationals and three Twenty20 games in Abu Dhabi and Dubai.
Ashraf discussed hosting the Tigers with Bangladesh Cricket Board president Mustafa Kamal last week, and a security team from Bangladesh will visit Pakistan in January, ahead of a potential tour in April.
"It's like breaking the ice," Ashraf added. "They will be meeting with top security officials of our government. We want to remove this security fear.
"Even if [Bangladesh] play two or three matches, it will send positive signals to the cricketing community around the world."
Six police officers and a driver were killed, and several players and officials injured, when gunmen opened fire on the Sri Lanka team bus on its way to the Gaddafi Stadium for the third day of the second Test.
All 27 of Pakistan's Tests and their 67 one-day internationals since the terror attacks have been played on foreign soil, and the World Cup games scheduled to be staged in the country earlier this year were moved for security reasons.
The UAE has served as Pakistan's temporary home, although Lord's and Headingley hosted two Tests against Australia in 2010.
Meanwhile, Pakistan have confirmed that Mohsin Khan will continue as interim coach for next month's Test and one-day series against England.