A deal would mark the latest move by a Japanese firm to hive off struggling divisions to repair their finances, with Toshiba and Sony among a string of companies that have sold off assets in recent years.
Japanese personal computer makers have been scaling back their businesses as consumers move to mobile devices to check e-mail or use the web.
The leading Nikkei business daily said the merger was among a number of options Fujitsu was considering for the money-losing unit. It did not give financial details.
The firm's Tokyo-listed stock surged nearly six percent to close at 568.7 yen today.
Fujitsu has been struggling to find a partner for its PC unit. It had been in talks with Toshiba and Vaio to merge their once high-flying personal computer businesses, but the talks have yet to result in a deal.
The reports today from the Nikkei and other Japanese media said Fujitsu and Lenovo were aiming to reach a deal by the end of this month as Fujitsu looks to focus more on its IT services business.
Another option could see Lenovo taking a majority stake in Fujitsu's PC subsidiary, it said, adding that either move could see about 2,000 Fujitsu employees move over to the Chinese company.
Lenovo already has a PC joint venture with Japan's NEC.
Hiroshi Sakai, a chief analyst at SMBC Friend Research Center, warned Fujitsu may be running out of time to find a buyer for its PC unit in a shrinking market.
Still, he added that its focus on corporate clients and its facilities in Japan could be attractive for a potential suitor.
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