Breeden said if his slate is elected, he would urge H&R Block to sell non-core assets, including businesses unrelated to tax preparation.
Kelly Flynn, a UBS Securities analyst, called Breeden's move consistent with her expectation that H&R Block will face "mounting pressure" from shareholders to consider a recapitalization, or being acquired by a private equity firm.
She said H&R Block could be worth $29 per share, excluding its mortgage unit, in a leveraged buyout.
For the fourth quarter ended April 30, H&R Block posted an $85.6 million loss, largely stemming from a write-down for its Option One Mortgage Corp. subprime lending unit.
The quarter is normally H&R Block's most profitable, encompassing most of the main U.S. tax filing season.
H&R Block is selling Option One to private equity firm Cerberus Capital Management for as much as $800 million.
The price is tied to the unit's value at the time of sale, which is expected to close in October.
Breeden was chairman of the SEC from 1989 to 1993. Earlier this year, he won two seats on the board of Applebee's International after complaining of poor performance at the casual dining restaurant chain.