If approved by the two governments, the series would likely be three one-day internationals in December-January.
"It was decided to resume cricketing ties with Pakistan by inviting the Pakistan cricket team for a short series in December 2012-January 2013," the Indian cricket board, the BCCI, said in a statement.
"The modalities will be worked out shortly."
The rivals have not played a series since Pakistan's tour of India in 2007 after cricket ties were snapped following the 2008 terror attacks on Mumbai, which were carried out by militants from Pakistan.
The games will be in New Delhi, Mohali and the Himalayan hilltown of Dharamshala, between December 23 and January 10, news reports said.
They will be sandwiched between England's tour of India.
The Pakistan Cricket Board (PCB) swiftly welcomed the proposed series, which will now require approval from the Indian foreign affairs and home ministry.
PCB chairman Zaka Ashraf told local television channels that Pakistan was still waiting for a formal invitation, but said "it seems it will surely be held later this year".
Cricket ties have been the subject of discussions between the governments of both nuclear-armed countries, who have been holding regular meetings in a bid to improve ties and eventually thrash out a peace agreement.
The countries have fought three wars since independence in 1947.
The Indian and Pakistani cricket teams have only met in international tournaments since 2007.
They clashed in the World Cup semifinal in the north Indian town of Mohali last year, a high-profile game that was attended by the Prime Ministers of the two countries.
They also played during the Asia Cup in Bangladesh in March. Both matches were won by India.
An Indian government source said the decision to resume cricket ties was made by the respective boards and not the government.
"The issue of resuming cricketing ties came up in recent bilateral talks and it was left upon the boards to resolve it," the source said.
"Once they have decided, then there would be the issue of internal security, which will be reviewed and decided by various agencies.
"The clearance by the ministry of external affairs will be done only after internal security issues are resolved.
"So far they (boards) have not even approached us."
In a gesture hailed as a positive signal, the BCCI in May invited a Pakistani team to take part in the inter-club Champions League Twenty20 tournament, which the Indian board owns with the boards of Australia and South Africa.
Pakistan's champion Twenty20 side, Sialkot Stallions, will participate in the tournament that will be held in South Africa in October.