E*Trade Financial Corp.’s mortgage albatross is loosening to the point that acquirers may start to get comfortable with the idea of a takeover.

The online brokerage has been scaling down its home-loan portfolio since the subprime mortgage market started to deteriorate as the financial crisis unfolded in 2007. Back then, E*Trade customers owed more than $27 billion. The current balance—$6 billion—is far less burdensome. Regulators also recently determined that the lending unit is healthy enough to no longer require capital support from the brokerage side, which has helped propel the stock to a more than six-year high.