Wood met FCB's chief executive, John Banks, and its managing director, Jonathan Rigby, on Tuesday to tell them he wanted to hear other agencies' views about the brand's future direction.
FCB has been invited to join the pitch, which is being conducted by the Haystack Group, but has yet to make up its mind.
The move coincides with the sudden departure of Bill Humes, the Weetabix commercial director.
Wood, the former Muller Group managing director who joined Weetabix this summer, has a reputation as a "hands-on" operator who likes to have direct control of marketing operations.
Humes, along with Richard George, the former managing director and now the company's non-executive chairman, was a key player in the 2001 appointment of the then Banks Hoggins O'Shea/FCB.
Weetabix was synonymous with the long-running "Withabix, Withoutabix" campaign when FCB took over the business, then backed with a £30 million spend, from Lowe. Sales had been suffering because of changing breakfast habits. However, the brand's fortunes have improved in recent years and in 2002, it overtook Kellogg's Corn Flakes as the UK's biggest cereal brand, with advertising under the theme "Generating energy for everyone".
Banks said: "Our Weetabix advertising could be better but, in terms of the business, we've done all that's been asked of us. Its loss would be a financial and an emotional blow but Wood wants to hear others' views and, if I were him, I'd probably be doing the same thing."