The BCCI is monitoring the situation and is also in touch with the state government and a final decision is expected to be taken soon.
Protests have been going on various cities of Tamil Nadu, including Chennai over the UN resolution on Sri Lankan war crimes against Tamils.
There are reports that some of the IPL franchises have requested the Governing Council to drop Chennai as a venue, citing security of the Sri Lankan players.
"We are aware of the situation in Tamil Nadu and we will take a decision soon. But as of now, we are not thinking of shifting matches out of Chennai", the official said.
Altogether 13 Sri Lankan players, two of whom are captains of their respective teams, are taking part in the sixth edition of the league which will start from April 3.
The upcoming elections in Karnataka could also force the IPL to tinker with the schedule as some of the matches in Bangalore may be affected during the run-up to the election.