The decision comes two weeks Indian Prime Minister Manmohan Singh and his Pakistani counterpart Yousaf Raza Gilani watched together as their respective teams played in the semi-final of the Cricket World Cup in northwest India.
Several Indian newspapers cited unidentified government sources as saying the question of precisely when and where the first cricket series between the rivals might take place would be decided by the two national cricket boards.
Although the Indian and Pakistani cricket teams have played each other in international and regional tournaments in recent years, the last series was held in 2007-08, when the Pakistani team visited India.
India broke off diplomatic and sporting links after 10 gunmen launched coordinated attacks on targets in Mumbai, killing 166 people in November 2008. India blamed Pakistan-based militants for the assault.
The Mint newspaper quoted one government source as saying India's cricket team would tour Pakistan next year, with a return series in India the year after.
The Board of Control for Cricket in India (BCCI) said it had yet to be formally notified of the decision to resume cricket ties.
"We have not received any government announcement as yet, so the board has not discussed the matter," BCCI chief administrative officer Ratna Karshetty told AFP.
No international cricket team has visited Pakistan to play any match since militants launched a gun and grenade assault on the visiting Sri Lankan cricket team on March 3, 2009.
The attack saw Pakistan stripped of its right to co-host the just-concluded 2011 Cricket World Cup.
IS Bindra, principal advisor to the International Cricket Council, said the resumption of direct cricket ties was a "welcome step."
"It's a nice thing not only for India, but for world cricket as a whole that Pakistan will come into the mainstream of world cricket," he said.
Former Indian all-rounder Madal Lal also welcomed the move, but said the authorities would have to guarantee the safety of players touring Pakistan.
"It is always good for the game when India and Pakistan play each other," Lal said.
"But the Indian government must be very careful. They must ensure that the situation is conducive for cricket in Pakistan."
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