Indian Foreign Secretary Subrahmanyam Jaishankar was willing to attend talks on the invitation of his Pakistani counterpart, the sources said, adding that they should focus on the situation in Kashmir, according to Reuters.
The olive branch comes after 40 days of violent protests in Indian-ruled Kashmir that were sparked by the killing by security forces of a field commander of Pakistan-based militant group Hizbul Mujahideen who enjoyed wide support.
At least 64 people have died and thousands been injured in clashes with security forces that have been denounced by Pakistan, which also claims the right to rule Jammu & Kashmir in a territorial dispute that dates back to partition in 1947.
In the latest clash Wednesday, militants killed three members of the security forces when they ambushed an army convoy and then fired on a police jeep that came to the scene.
The Indian sources made it clear, however, that India "rejects in their entirety the self-serving allegations regarding the situation in J&K, which is an integral part of India."
Jammu and Kashmir (J&K) is the name of the Indian state that includes the disputed Kashmir region.
Indian Prime Minister Narendra Modi ratcheted up tensions in his annual Independence Day speech Monday, accusing Pakistan of glorifying terrorism.
And, in a tit-for-tat escalation in the war of words between the nuclear-armed neighbors, Modi said he had received messages of support from leaders in restive regions of Pakistan, in particular the troubled southwestern province of Baluchistan.
India accuses Pakistan of supporting Kashmiri fighters while Pakistan accuses India of meddling in Pakistani trouble spots, in particular of helping separatists fighting the Pakistani state in resource-rich Baluchistan.
Both sides deny the accusations.