The Indian government stopped its team from touring Pakistan early last year for a test series and since then the two countries have only played in the Champions Trophy one-day tournament in South Africa last year.
"One of the things I am working on is trying to persuade the BCCI (Indian cricket board) that they should play bilateral matches with Pakistan as opposed to just in ICC events," Morgan told the News broadsheet on Tuesday. "Pakistan versus India is equivalent to the Ashes. It is very important for both countries that they renew their rivalry on the field in the five-day game. I am very hopeful they will."