In the unexpected announcement, the California Republican said the measure would not only address the entitlement program's long-term fiscal solvency but also pension and tax reforms.
He also expressed optimism about the concept of lowering benefits for wealthier retirees as a means to cut costs, as President Bush proposed Thursday.
The Senate has been expected to take the lead in drafting Social Security legislation, with the House possibly waiting to respond to the Senate proposal.
Thomas did not commit to including the president's plan for private investment accounts funded through payroll taxes.
One alternative idea that has been floated is making private accounts add-ons to the program, funded through another mechanism.
"Personal accounts can take a number of forms, and we're going to examine all those that have been offered," said Thomas.
House and Senate Democrats remain opposed to adding such accounts to the program, saying the concept must be taken off the table before any bipartisan discussion of legislation can begin.