The 29-year-old West Indian spinner faced an uncertain future last month when his bowling action was again reported during the Pakistan Super League.
"I had some very good conversation with the IPL, there's absolutely no issue with Sunil. He's joined the side, it's business as usual. No worries there," Mysore said on the sidelines of a promotional event.
Australian left-arm seamer Starc, who was bought by KKR for Rs 9.4 crore, has been ruled out after suffering a stress fracture.
"We are not yet ready to make the announcement. Protocol demands that the IPL announces it first, hopefully by tomorrow (you will get the name)," he said, even as there is speculation that West Indies captain Jason Holder will be named as Starc's replacement.
The team CEO said they are not worried too much because of Starc's injury pullout and said Mitchell Johnson would lead the attack.
"We have a very good option in Mitchell Johnson. He has played more IPLs and won two championships when he has played for teams and he is an outstanding player.
"He bowled well in the Big Bash, he is still fit, and bowling 145kph plus. He is an experienced campaigner, I don't think we won't miss him (Starc) initially but we need backup," he said about the Perth Scorchers pacer who bagged seven wickets from 10 matches at an average of 36.28.
"It's funny how injuries are beyond anybody's control. You hope that it doesn't happen but you are ready. So it's not about big names to be honest.
"In 2012, nobody had even heard of Sunil Narine. He came and took IPL by storm. So something like that could happen and I always feel in every adversity there is an opportunity. So there may be someone who can come and surprise us. We are disappointed but not that much," Mysore said.
The Aussie duo of Johnson and Chris Lynn are on their way and will join the side tonight.
"Tomorrow we will have a practice game. They might play tomorrow. They will be available for the first game," he added.
KKR open their campaign against Royal Challengers Bangalore on April 8.
(With PTI inputs)