The former Karnataka minister said the letter purportedly written by Siddhartha, "which is circulating", is dated July 27 (Saturday) and he received a call from the son-in-law of former Karnataka chief minister and BJP leader S M Krishna on Sunday asking if they could meet.
Siddhartha had left from Bengaluru to Sakleshpur in Hassan district on Monday afternoon, but he asked his driver to turn towards Mangaluru on the way, according to police.
He was last seen near a bridge on Netravati river in Dakshina Kannada district on Monday night. He had told his driver he was going for a walk near the bridge, police said.
"It's unbelievable that a courageous man like him would resort to this," Shivakumar tweeted. He said he has known closely Siddhartha and his family members for decades.
"However, I find this (the disappearance) utterly fishy and urge that a thorough investigation be conducted into this matter," he said.
In a letter purportedly written by Siddhartha to the Board of Directors and employees of Coffee Day Enterprises, he said: "I have failed as an entrepreneur."
There was no immediate confirmation on whether the letter was written by him, though it was written on his letter head with signature.
In the letter, Siddhartha said, "I would like to say I gave it my all. I am very sorry to let down all the people who have put their trust in me."
He said he fought for a long time, but "today I gave up as I could not take any more pressure from one of the private equity partners forcing me to buy back shares, a transaction I had partially completed six months ago by borrowing a large sum of money from a friend".
"Tremendous pressure from other lenders lead to me succumbing to the situation," he said.
He alleged in the letter that there was a lot of harassment from the previous DG, Income Tax Department, in the form of attaching "our shares on two separate occasions to block our Mindtree deal and then taking possession of our Coffee Day shares, although revised returns have been filed by us."
"This was very unfair and has led to a serious liquidity crunch," he said.