The newspaper said Monday Kushner's bid was confirmed by a person familiar with the sale process but not authorized to discuss it. Kushner and a Dodgers spokesman could not be reached for comment, the Times said.
Kushner has plenty of competition, the New York Daily News reported Tuesday. A group headed by basketball star-turned-businessman Magic Johnson and another headed by former New York Yankees manager Joe Torres are among the eight other potential buyers, the Daily News said.
If he succeeds, Kushner, 31, would be the youngest owner in Major League Baseball.
The team is in bankruptcy and up for sale largely because of the messy divorce proceedings between its current owners, Frank and Jamie McCourt.
The deadline for a sale is April 30.
Kushner, who married Ivanka Trump in 2009, is owner-publisher of the New York Observer.
The Times said its source said Kushner is working with UBS Vice Chairman Aryeh Bourkoff in putting together the offer. While the deal would be financed primarily by the Kushner family, it would not include his father, who served a prison term for illegal campaign contributions, the Times said.