The Gold family trust owns 25.1% of the shares in the Championship club, who were relegated from the Premier League last season.
"I have now reached an agreement to sell my family's shareholding to a consortium of PCP Capital Partners, led by Amanda Staveley and Mehrdad Ghodoussi, in partnership with Ashland Forest Capital Partners," Vanessa Gold said in a statement on Saturday.
"This sale remains subject to a pre-emption process, under which existing shareholders have the option to buy the shares instead. While the process has not yet concluded, I wanted to be open with our fans about where things stand and my intentions."
David Sullivan is the club's biggest shareholder, with 38.8%. Kretinsky, through 1890s Holdings, owns 27% and would have become the majority shareholder had the agreement to buy a 16% portion of the Gold family's shares gone through.
"On the 12th June Daniel Kretinsky and I agreed a sale (...) unfortunately, since that time the original deal and other alternatives that we have discussed could not be brought to fruition," Gold said.
Staveley and her firm, PCP Capital Partners, had played a key role in helping Saudi Arabia's Public Investment Fund (PIF) take over Premier League club Newcastle in 2021.
"The Consortium will bring deep experience and understanding of what it takes to lead a successful football club, and I have every confidence in what they can bring to West Ham," Gold added.