"Coach selection has been entrusted to the CAC (Cricket Advisory Committee), which selected Anil Kumble last year for a one-year contract. Now the process has to be followed. But since the process has been delayed, Kumble, subject to his accepting, will be there for the West Indies tour," Rai told reporters here.
"The CAC is meeting in London to decide upon the road ahead," he added.
Kumble's current one-year contract with the Board of Control for Cricket in India (BCCI) will expire on June 18, when the final of the ongoing Champions Trophy is to be held.
India's tour of the West Indies, which will include five One-Day Internationals (ODI) and a single Twenty20 International is scheduled to run from June 23 to July 9.
Doubts have been raised on Kumble's chances of bagging a renewed contract as coach of the national team following reports of a rift with a few senior members in the India squad, including captain Virat Kohli.
Kumble's demand of a steep hike in his own salary as well that of the players has also reportedly drawn the ire of several BCCI officials.
Rai, however, insisted that reports of a rift between Kohli and Kumble have been blown out of proportion.
"The fact is that it was a one-year contract, so a process was followed. I don't know why the controversy. I have spoken to both of them and neither of them has confirmed what has come out," Rai said.
"How can the situation be handled better? The fact that the contract is for one year was known, so why the controversy?" he added.
CAC members Sachin Tendulkar, V.V.S. Laxman and Sourav Ganguly are in London and are scheduled to meet both Kumble and Kohli before coming out with a decision.
"We have left it to the CAC, they are legends, they know what is best for Indian cricket," Rai said."The CAC will have meeting in London and deliberate on future course."
Former CoA member Ramchandra Guha had mentioned several instances of alleged conflict of interest in the working of the BCCI, including Rahul Dravid's role as India A and India U-19 coach as well as mentor of the Delhi Daredevils team in the Indian Premier League (IPL).
"All issues regarding conflict of interest will be referred to the ethics officer appointed by the BCCI. He will be appointed soon. A lot of complaints regarding conflict of interest have been received," Rai said.
"Guha's letter will be discussed in the SC (Supreme Court) as we are a court appointed agency and we owe our explanation only to the court," he added.