The ICC's current $550 million seven-year deal ends with next year's World Cup in West Indies and world cricket's ruling body began last week negotiating new sponsorship until 2015.
"We have written to the ICC expressing our interest," Board of Control for Cricket in India (BCCI) secretary Niranjan Shah said on Monday.
ICC's global events for the period 2007-15 include two World Cups, the first of which in 2011 is to be hosted by the sub-continent.
The BCCI signed its own media rights contract worth $612 million in February, making it one of the world's richest cricket bodies and the country the game's commercial centre.
It expects revenue from all its rights deals to top $1 billion over the next four years.
No cricket board has previously bid for the governing body's global rights but the BCCI feels that as co-host of the 2011 World Cup it will be in the best position to generate maximum revenue.
The BCCI is meeting on Tuesday to discuss the ICC's mandatory agreement for participation in global events that it had declined to sign unless certain clauses were amended.
India's endorsement-rich players were at the centre of a major contract row before the 2003 World Cup, arising from the conflicting interests of official tournament sponsors and the team's personal ones.
They finally signed an amended contract and were allowed to play.
