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.

E*Trade could pay up to $16.50 a share for Ameritrade, analyst Rich Repetto at Sandler O'Neill & Partners estimated, based on his assumptions for around $562.1 million in synergies and combined net income of $1.15 billion next year.

"While we still do not believe a deal is imminent, this new information has the potential to shorten what we thought would be a longer timetable for Ameritrade's acquisition/merger," Repetto told clients. He expects the companies to be worth nearly $14 billion combined.

Analysts had been predicting that discount brokerages were ripe for merger deals as trading volumes from customers remain weak. Intense competition for accounts has kept the pressure on commissions that the brokers can charge for some time.

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