The six-nation tournament was originally scheduled to be held in late April at the end of India's first Test series in Pakistan in almost 15 years.
But the Asian Cricket Council (ACC) abandoned the idea when told by India it had a commitment to play a Test series in Bangladesh soon after the Pakistan tour.
ACC chief executive Ashraf-ul Haq said a July date was being considered for the tournament which features India, Pakistan, Sri Lanka, Bangladesh and two qualifiers, the United Arab Emirates and Hong Kong.
"There is a period between July 11 and the first week of August when all six teams will be free, so we may schedule it then," Haq told.
"Pakistan is the only team that has not confirmed so far for July, but we are confident they will agree."
The biennial tournament has not been held since the May 2000 event in Dhaka due to political tensions between India and Pakistan.
It remains to be seen if Pakistan, the original hosts of the 2004 tournament, can hold it in July due to the onset of the monsoons and hot weather in that period.
Sri Lanka is the only country in the region which organises International cricket in the month of July.
The Board of Control for Cricket in India (BCCI) officials, meanwhile, will meet in Kolkata next week to finalise the itinerary of the Pakistan tour in March-April for, possibly, three Tests and five to seven One-day Internationals.
India last played a Test series in Pakistan in 1989, while Pakistan crossed the borders in 1999 for three Test matches.
BCCI dismisses threat to Pak tour