Proposals announced yesterday would also allow the watchdog to suspend an individual from trading for up to two years.
The changes are part of a major clampdown by the FSA on financial impropriety in the wake of the financial collapse.
The FSA, whose enforcement unit is led by Margaret Cole, will also seek powers to fine those found breaking short-selling rules. Short selling became a highly politicised issue after several western nations blamed the practice for exacerbating the financial downturn.
The proposals are a statement of intent from the FSA, which could be abolished if a Conservative government is elected next week. Both Labour and the LibDems would keep the watchdog. The Tories argue FSA duties could be undertaken more efficiently by the Bank of England and a new financial crime organisation. The body had a record year last year, handing out more than £33m in fines. It has started 2010 with a string of arrests for alleged insider dealing.