The pacer decided to pull out of the auction in order to spend time with his family at home.
As per a report published in ESPNcricinfo, franchises were informed at a briefing in Chennai on Wednesday (February 17) that the pacer had decided to withdraw his name in order to spend time with his family at home.
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Wood was among the eight overseas players who chose to be slotted in the highest base price of INR 2 crore.
Meanwhile, Wood and wicketkeeper Jonny Bairstow have joined England's squad in Chennai ahead of the third Test against India.
"The pair have rejoined the England men's cricket team after time at home," England and Wales Cricket Board (ECB) had said.
The duo had also attended "their first training session after coming out of quarantine".
On Tuesday (February 16), India levelled the four-match Test series 1-1 against England after an emphatic 317-run win in the second Test at Chepauk.
The third Test will begin on February 24 in Ahmedabad and it will be a day-night affair.