Steinbrück is to make the proposal Monday at a crunch meeting of leaders of Chancellor Angela Merkel's "grand coalition" government aimed at hammering out an agreement on a major new economic stimulus package, the spokesman said.
The daily Süddeutsche Zeitung reported Friday that Steinbrück's Social Democrats would also call at the meeting for an increase of tax-exempt annual income to €8,000 ($10,800) from €7,664.
With the two measures, "the lowest income group can see targeted relief," the report said, quoting Social Democrats preparing for Monday's meeting. The moves would cost the state some €4.7 billion per year, the paper said.
The Social Democrats had initially rejected urgent calls by the Christian Social Union, a conservative partner in the ruling coalition, to slash taxes to get Europe's economic powerhouse moving again. But they have climbed down from that position in recent days.
The left-right government is under pressure to help Germany out of what many economists believe will be its worst downturn in six decades. The new stimulus package is expected to be worth some €50 billion over two years.
This follows a first raft of measures worth over €30 billion agreed in November that was widely derided by critics as packing too little punch as it included only €12 billion of real new spending.
Berlin has been widely criticised by other major economies for acting too slowly and too cautiously to face up to the financial crisis.