ENG v SA (1)
CWC League 2 (1)
IRE v AFG (1)
Women's Hundred (2)
Men's Hundred (2)
BAH v KUW (2)
WI v NZ (1)
RL Cup (8)
NL v PAK (1)
The inaugural IPL competition - from April 18 to June 1 - clashes with the first six weeks of the domestic season in England, while the national team are at home to New Zealand during the same period.
"Most of the English players say they'd like to play," Modi told BBC Sport. "It's not that we couldn't sign them [but] because it directly conflicts with the English games.
However, an ECB spokesman said England's commitments to the Future Tours Programme [FTP], which concludes in 2012, would result in its 12 centrally-contracted players missing out on the IPL.
Modi said the IPL would look at rescheduling its dates in the coming years in order to accommodate English players. "Sooner or later we will look at adjusting our programmes while we try to bring our league forward," he said. "The objective would be in the future we would be working with the ECB to ensure the overlap doesn't take place."
He also said that with top international stars opting for the IPL, county cricket in England would suffer. "They have decided to sign with us over and above the counties. The counties are going to be deprived of these players going forward."
One of the conflicts to have emerged already involves David Hussey, who has an existing contract with Nottinghamshire. Hussey was bought for a whopping $625,000 deal with the IPL's Kolkata franchise, and has indicated he will play for them as opposed to the county.
"We were expecting him to come to us in the middle of April," Mick Newell, Nottinghamshire's director of cricket, said. "We all want to work towards a compromise. David is keen to play in the IPL, the sums people are talking about are mind-blowing for cricket, so I'm sure both sides are keen to find a solution."
Modi suggested players didn't need permission from the county they are contracted with to play in the IPL. "David Hussey has nothing to do with Nottinghamshire, as far as we are concerned he only needs an NOC [No Objection Certificate] from his home board."