US reports say that Blamer is in talks to take on either the New York chief executive's job or, alternatively, chief executive of FCB's North American operation. Both jobs are current unfilled.
The FCB New York CEO job became open when Jeff Tarakajian relinquished his dual role of president and CEO in order to concentrate on new business as president of FCB New York.
Blamer's appointment to either role would set him up as the eventual successor to Brendan Ryan, chief executive of FCB Worldwide.
A spokesman for FCB would only say that the agency was currently looking to fill a number of senior roles.
Blamer has been running the New York office of Grey for three years after returning to the US following a two-year stint running Grey London, which he joined from Los Angeles.
He had been due to stay in London for at least another year, but was recalled to New York to boost the performance of Grey Global's flagship office.
His departure from London led to the short-lived appointment of Martin Smith, who departed after a year, leaving an 18-month gap before Garry Lace from TBWA\London was appointed as chief executive.
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