Billionaire Mark Walter purchased a majority stake in the NBA team last year in a deal that valued the club at $10 billion, with the deal only having been approved by the board of governors in October.
Reuters was not immediately able to reach the Lakers for comment.
The news comes weeks after Kushner became a key figure in a private equity fracas that has engulfed global soccer governing body FIFA, as it announced plans last month to create a subsidiary to run the World Cup.
FIFA had planned to sell minority stakes at an equity valuation of $20 billion to Kushner's Thrive Capital, in a move that sparked widespread outrage and imperiled FIFA President Gianni Infantino.
Iger, the former CEO of the Walt Disney Company, previously took a majority stake in NWSL side Angel City FC.