If granted, the seat will be given to Trian's chief investment officer Ed Garden, according to the report.
Last week, Garden said that GE CEO John Flannery, the 56-year-old who turned around GE's healthcare business before succeeding longtime CEO Jeffrey Immelt on Aug. 1, "is part of the solution" at the multinational conglomerate.
But, Garden has also acknowledged that the company must take a hard look at its portfolio of assets.
Trian owns a $1.7 billion stake in GE and has urged for improved profits.
Shares of General Electric were sinking in after-hours trading on Tuesday.
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