Microprocessors on a circuit board displayed at the Mobile World Congress in Barcelona, Spain, March 2, 2015.

Paul Singer's Elliott Management is adding to its bet on one Apple supplier.

The activist hedge fund bought 4.06 million shares of NXP Semiconductor in the third quarter, a filing with the U.S. Securities and Exchange Commission showed Tuesday.

That increases Elliott's stake in the chipmaker to 16.44 million, worth about $1.86 billion at Tuesday's prices. NXP Semiconductor is listed as one of Apple's suppliers in a February document.

Qualcomm is in the process of acquiring NXP, and Qualcomm rejected Monday an unsolicited takeover offer of more than $100 billion from Broadcom.

Elliott also increased its holding in Hess by 2.32 million shares to 21.12 million shares, but dissolved its 2.01 million share investment in BHP Billiton.

The filing also showed Elliott initiated a 2.3 million share stake in mall operator Taubman Centers.

The activist fund has spoken with management of the real estate investment trust about pursuing potential options that include going private, a source familiar with the situation told CNBC ahead of the filing's release.

— CNBC's Robert Hum contributed to this report.