Intel's marketing team is believed to have handed a brief to agencies to come up with ideas for the new product, a move which could loosen the close relationship between the agency and the client.
Eric Kim, Intel's chief marketing officer, is believed to have invited the agencies to pitch over the next few weeks.
The move comes as Intel yesterday announced its first job cuts as part of strategic review across the company, with as many as 1,000 redundancies planned among managers worldwide.
Reports state that Kim has been in talks with Omnicom Group's TBWA\Worldwide and BBDO Worldwide, as well as WPP Group's Berlin Cameron United and Young & Rubicam, although not all are expected to pitch for the Core 2 Duo work.
McCanns scooped the $300m (£163m) account in March last year after it beat WPP Group agencies in a pitch.
At the time, McCanns' win was a surprise because Kim was reported to get on well with WPP chief executive Sir Martin Sorrell. However McCanns won in the long drawn-out process with its "people love technology" pitch.
The account has previously been handled by Euro RSCG Worldwide and Media Planning Group, but both agencies pulled out of the review in January 2005.
Euro RSCG had handled the account since 1991, although the famous TV campaign featuring the Intel chime and tagline "Intel inside" was created by Dahlin Smith & White in Salt Lake City, which Havas acquired.
A campaign created by McCann featuring celebrities sitting on the laps of Intel computer-users launched in eight countries in September last year. Stars included John Cleese, actress Lucy Liu, skateboarder Tony Hawk and singer Mariah Carey.
West End theatre production Blue Man Group appeared in an Intel Pentium III campaign in the late 1990s.
Michael McLaren, worldwide account director for McCann WorldGroup, denied that Intel was looking outside of the agency and said the relationship between the client and agency was "healthy".
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