Jan 26 (Reuters) - A blank-check acquisition firm backed by veteran investment banker Alan Mnuchin is in talks to merge with digital health startup Sharecare Inc and take it public, people familiar with the matter said on Tuesday.

Under the terms of the proposed deal, Sharecare would buy Palo Alto-based healthcare artificial intelligence startup Doc.ai and then merge with Mnuchin's special purposed acquisition company (SPAC) Falcon Capital Acquisition Corp , the sources said. The deal with Falcon would value the combined entity at close to $4 billion, one of the sources added.

Mnuchin is the brother of former U.S. Treasury Secretary Steve Mnuchin. The transaction could be announced as soon as this week, the sources said, cautioning that negotiations might still falter.

The sources requested anonymity because the matter is confidential. Representatives for Sharecare, Falcon and Doc.ai did not immediately respond to requests for comment.

Sharecare, founded in 2012 by WebMD founder Jeff Arnold, is an online healthcare data platform that gives customers advice on health and lifestyle-related matters through a mobile app.

A SPAC is a shell company that raises funds in an IPO with the aim of acquiring a private company, which then becomes public as result of the merger. For the company being acquired, the merger is an alternative way to go public over a traditional initial public offering.

Falcon raised $345 million in an initial public offering in September on the Nasdaq stock exchange. Hollywood executive Jeff Sagansky, former SoftBank Vision Fund managing partner Michael Ronen, hedge fund Metropolitan Capital Advisors founder Karen Finerman and Waverley Capital founder Edgar Bronfman sit on Falcon's board. (Reporting by Anirban Sen in Bengaluru and Joshua Franklin in Miami Additional reporting by Rebecca Spalding in New York; Editing by David Gregorio)