Xerox has made a cash-and-stock offer for HP, which is significantly larger than Xerox. Photo: Michael Nagle/Bloomberg News

Shares of Xerox Holdings Corp. XRX 3.13% and HP Inc. HPQ 10.03% rose after The Wall Street Journal reported on a possible tie-up of the legacy technology companies.

Xerox has made a cash-and-stock offer for HP, a big personal-computer and printer maker, people familiar with the matter said Wednesday. The Wall Street Journal reported late Tuesday that a bid might be forthcoming.

On Wednesday morning, shares of HP were up 12%, while Xerox shares were up 1.7%, in a sign that shareholders of both companies might approve of a union.

HP, which had a market value of about $27 billion as of Tuesday’s close, is significantly larger than Xerox, whose market capitalization was about $8 billion. The bid includes a takeover premium and is less than $23 a share, the people familiar with the matter said. HP stock closed Tuesday at $18.40.

The big question now is how receptive HP is to the offer. The company hasn’t made any public comment about the overture.

A deal would join two household names with storied pasts that have been trying to retool their businesses as the need for printed documents declines. Both companies are in cost-cutting mode and a union could afford new opportunities to shed expenses—to the tune of more than $2 billion, according to people familiar with the matter.

JPMorgan Chase & Co. analyst Paul Coster said in a research note that the deal looks feasible and has merit, adding that Xerox Chief Executive John Visentin is well-equipped to cut costs and restructure a combined company. He said a merged entity could innovate faster. The drawbacks, however, would be the size and complexity of the deal, he added.

“The combined company will still be confronted with the challenge of mid-single-digit secular decline in printing industry revenues,” Mr. Coster said. “Execution of cost synergies could take 2-3 years to realize, and there are risks associated with the undertaking.”

Billionaire investor Carl Icahn, who owns a 10.6% stake in Xerox and along with a partner controls its board, would likely play a big role in the outcome.

“The question now is whether Icahn (or someone else) is also on the other side and in a position to put pressure on [HP’s] new CEO, Enrique Lores, ” Gordon Haskett analyst Don Bilson said in a research note. Mr. Bilson also said that should HP not be receptive, the window for a shareholder to launch a proxy fight for board seats opens on Christmas.

Should Xerox acquire HP, it could be the second recent example of Mr. Icahn orchestrating a deal in which the buyer is smaller than the seller. Eldorado Resorts Inc. in June agreed to acquire Icahn-backed Caesars Entertainment Corp. , which is twice its size, for roughly $9 billion.

Write to Patrick Thomas at Patrick.Thomas@wsj.com and Cara Lombardo at cara.lombardo@wsj.com

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