The bid is sharply higher than the $1.13 billion offer announced last week by HP rival Dell Inc., the Los Angeles Times reported Monday.
The bid may offer insight into HP's long-term strategy, given the resignation of Chief Executive Officer Mark Hurd, who left this month after reportedly filing false expense statements to cover up a relationship with a former contractor who had accused Hurd of sexual harassment, The Huffington Post reported.
3Par Inc. produces data management software for corporations. Acquiring the company would put HP or Dell in a stronger position regarding software subscription sales, the newspaper said.
Dell's $18 per share bid was already well above 3Par's market value. On Monday, 3Par's share price rose to $25.35, a 41 percent jump.
HP's offer comes to $24 per share.