The ties had been snapped after the 2008 Mumbai terror attacks and there have been several attempts by the Pakistan Cricket Board in recent months to convince the BCCI.
The planned series is subject to government approval.
"The government is ready in principle to host the Pakistan team", a top BCCI official said after the Working Committee meeting here.
The PCB had earlier proposed that either India tour Pakistan or play them at a neutral venue.
Resumption of Indo-Pak bilateral cricket ties got a boost after the foreign secretaries of both the countries asserted that sporting relations should be strengthened.
The thaw in the relations had begun much before that when BCCI invited Pakistan's domestic Twenty20 champion Sialkot Stallions to participate in the Qualifying Tournament of Champions League Twenty20 to be held in South Africa later this year.
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During the recent visit of PCB chief Zaka Ashraf to India and at last month's ICC and Asian Cricket Council meetings in Malaysia, there had been discussions between officials of both the Boards on the matter.
India and Pakistan last played in a bilateral series in November 2007, in which the former beat the latter 3-2.
After that, there was no bilateral cricket between the two arch-rivals even though they did face each other in multi-team events like the World Cup.
Although the fixture of the three-match series is yet to be decided, Mohali and Chennai are the likely venues to host the matches. The third venue could be either New Delhi or Bangalore.