Modi said the Pakistani cricketers missed the bus by failing to get visas by the December 7 deadline and the IPL franchises have already replaced them with fresh recruits.
In such a scenario, the Pakistani cricketers can hope to be part of the event only through the next round of the players' auction, scheduled on January 19.
"Yesterday all the teams were required to do the replacement strategy and the replacement was allowed for those players who are not going to be part of the squad.
"Unfortunately the teams have already signed their replacements. Kolkata Knight Riders have already replaced Umar Gul with Charls Langeveldt, Misbah-ul-Haq (of Royal Challengers Bangalore) has been replaced by Roelof van der Merwe and there have been replacements in the Rajasthan Royals also. These replacement contracts have already been placed and cannot be reversed," Modi said.
The only ray of hope for Pakistani players, Modi said, is through the next auction.
"There is an option coming up on January 19. If there are spots open, they can then apply for the auction now. Because you have to go through the process; now the process for applying for auction is by January 1," he said.
Modi said the IPL had given its franchises the go ahead for new contracts after Pakistani players failed to get their visas before the deadline.
"As they missed the deadline, the new contracts have been signed and they (the franchises) have written back to us stating very clearly about the new contracts. It is a very difficult process to reverse the new contracts. We have a system and we cannot abuse the system," he said.
"The players can go to the auction pool now, because they have missed the trading pool, if any of the team wants to pick them up," Modi said.
He said he spoke with Minister of State for External Affairs Shashi Tharoor, who told him that four Pakistani players -- Sohail Tanveer, Misbah-ul-Haq, Kamran Akmal, Umar Gul -- had been granted visas by the government but they have to come as fresh recruits in the auction.
"The way auction pool works is that the franchises have to forward us the name of players. At present, they have got 140 players, who are eligible for auction. After shortlisting, the number will come down to 40-50. It would depend on the franchisee which player they want in auction pool," he said.
Modi said that the IPL board will take a call on January 17 on the contracts which have been terminated because of visa problems.
The IPL governing body has placed a cap of US $7,50,000 on the franchisees for the purchase of players.
Modi expressed hope that government's decision to grant visa to the Pakistani players will help in normalising the cricket ties between the two countries.
"It is a positive move and we are looking forward to that," the IPL Commissioner said.
"I hope so, sooner or later... but this is not something which I can answer right now. And that will be decided by the working committee of the Board," he said in reply to a question on Indo-Pak cricket ties.
Modi, however said, that as of now there is no such proposal and neither any cricket series has been scheduled.
"But I am sure when the time comes, they will take it up," he added.
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