Publicis won HP's UK online advertising business from WPP's Banner, as well as parts of its direct marketing held by Omnicom's Tequila\London, without a pitch after a decision taken by HP's Palo Alto head office.
Publicis refused to confirm or deny the wins.
The US agency Publicis & Hal Riney shares the global HP creative account with Goodby Silverstein and sources indicated Publicis is working hard behind the scenes to tie up as many areas of the HP business as possible.
Goodby Silverstein's grip on the account was potentially weakened in April when HP fired its chief executive and president, Carly Fiorina, and replaced her with the former NCR president Mark Hurd. Fiorina appointed Goodby Silverstein in 2003 and signed off its "HP Invent" series of ads.
Last month, Hurd appointed Cathy Lyons to replace the long-serving chief marketing officer and vice-president, Mike Winkler.
Following these changes, HP is said to be changing the focus of its advertising from brand-led to "demand-led" work focusing on specific product and sales needs.
HP is in a period of change and is looking to save more than $1.9 billion a year. It has started by cutting back more than 14,500 jobs worldwide.
An HP spokesman said: "We refuse to comment on rumours and speculation."