Online broker E*Trade Financial has made an unsolicited offer to buy rival discount broker Ameritrade Holding, according to reports Monday.

E*Trade made a bid for over $5.5 billion in a "bear hug" letter on Friday to the board of Ameritrade, The New York Times reported, citing executives involved in the talks. Separately, The Wall Street Journal reported top executives at the two companies have held exploratory talks over the past year.

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