English-language newspaper Dawn reported the sense of Afghanistan's willingness to consider Islamabad's offer, first made in 2010, came after a visiting Afghan defense delegation led by Defense Minister Gen. Bismillah Khan Muhammadi met with Pakistani army chief Ashfaq Pervez Kayani.
The delegation arrived in Islamabad last Sunday on a five-day visit, and Dawn said such a rare visit may indicate a shift away from Afghanistan's years of distrust of its neighbor over its alleged support of the Taliban insurgency.
Contacts between the two countries come as NATO and U.S. forces prepare to end their combat operations in Afghanistan by next year.
"Both sides showed understanding for the fact that not only the geography, history and culture, but also the destiny of the two countries was shared," a military source was quoted as telling Dawn.
"This makes it imperative for the two countries to move forward with a joint approach on important national and regional issues, and have a joint strategy on security issues affecting either of two countries, or both."
Separately, Pakistan's Express Tribune, quoting a senior military official, said the talks proved to be decisive as the two sides agreed to explore the possibility of "military training exchanges" as their relations improve, reducing years of trust deficit.
The official told the Express Tribune the Afghan delegation would visit military institutions to determine how the two sides can reach an accord to strengthen military-to-military contacts.
The report said a statement from Pakistan's Inter-Services Public Relations said the two sides discussed matters of professional interest, with particular focus on "enhancing mutual defense cooperation and measures that the Afghan National Army and Pakistan Army intend to initiate for an enduring training relationship."
In recent weeks, Pakistan also has released several Afghan Taliban prisoners to aid in Kabul's peace process. Pakistan's participation in the peace process is considered critical.
Notable deaths of 2014 [PHOTOS]