In addition to its current roster media agencies, Omnicom's OMD and Interpublic's Universal McCann, the company has invited MindShare to pitch for the account.
MindShare's WPP sibling, Ogilvy & Mather, handles advertising for Gillette's Duracell battery brand.
The review is part of a wider 'strategic sourcing initiative' by Gillette.
A Gillette spokesman said: "It is an internal assessment process, not a formal review. We've asked our existing agencies for info about their organisation, capabilities and resources. We've included MindShare because we've had a longstanding relationship with Ogilvy & Mather."
He added that while the review would take "a few months", a result was likely sometime in the third quarter, and stressed that creative relationships would be unaffected.
The review is being administered by a global Gillette team headed by vice-president, marketing services Dick Cantwell and including European media director Michael Winkler.
Gillette announced its strategic sourcing initiative last June. Shortly afterwards it consolidated its £56m global oral care account, including the Braun and Oral-B brands, into BBDO Worldwide, which already held the Gillette and Right Guard accounts. In the UK, that move shifted the £3.3m account from IPG's Lowe Lintas into Abbott Mead Vickers BBDO.
The initiative, led by chief executive James Kilts, is designed to put savings from agency and third-party suppliers into marketing core brands.
Kilts said at the time that the assessment was meant to help bring Gillette's adspend in line with that of competitors after a slide to 5.8% of global gross sales, and break what he called the "circle of doom, in which disappointing sales of new products push marketing expenditure ever lower. Kilts also promised to use savings to correct an imbalance in spend which favoured advertising over promotions.
With two-thirds of Gillette's media business, OMD is the most exposed of the agencies involved.