* New offer to clear Toshiba's 2 tln yen threshold - source
* Toshiba, Western Digital have been at loggerheads
* New offer seeks to clear antitrust concerns - source (Adds context, detail on arbitration)
TOKYO, June 10 (Reuters) - Western Digital Corp plans to raise its offer for Toshiba Corp's prized semiconductor unit to 2 trillion yen ($18 billion) or more, a person familiar with the matter said, marking a last-ditch effort to clinch a deal that both companies consider vital.
The U.S. chipmaker's new offer, to be presented by Thursday when the struggling Japanese conglomerate is to decide a preferred bidder for its Toshiba Memory Co unit, will be in the form of a debt purchase, to avoid antitrust concerns over the proposed acquisition of the world's second-largest producer of NAND memory chips, the person told Reuters on Saturday.
A spokesman for Western Digital had no comment. Toshiba could not immediately be reached for comment.
Toshiba had set a 2 trillion yen threshold for the sale. It is rushing to find a buyer to cover billions of dollars in cost overruns at its now-bankrupt U.S. nuclear business Westinghouse Electric Corp.
Western Digital, bidding in a consortium led by a Japanese government-backed fund, initially offered 1.6 trillion yen, sources have said. CEO Steve Milligan then raised the offer to "very close to 2 trillion yen" on Friday in a meeting with Toshiba CEO Satoshi Tsunakawa, the source said on Saturday.
But Toshiba also expressed dissatisfaction with Friday's bid. "Our concerns about the prospects of success for a deal were not wiped out," a Toshiba spokeswoman said.
That set the stage for the newest offer to potentially go over 2 trillion yen if required.
Western Digital has been seen by some sources as crucial to any successful deal, as it jointly operates a key flash-memory chip plant with Toshiba in western Japan.
But the two companies have been at loggerheads over the auction, with Western Digital pursuing an international arbitration claim that Toshiba has breached the joint venture contracts by entertaining outside bids and arguing that the sale cannot proceed without its consent.
Western Digital will drop its claim if Toshiba agrees to the new offer, the source said on Saturday.
Toshiba has been favoring a rival bid from U.S. chipmaker Broadcom Ltd, which has partnered with U.S. private equity firm Silver Lake to offer 2.2 trillion yen, people familiar with the matter have told Reuters. (Reporting by Makiko Yamazaki; Additional reporting by Liana B. Baker in San Francisco and Naomi Tajitsu in Tokyo; Editing by William Mallard & Shri Navaratnam)