Gingrich, the former U.S. House speaker, told reporters he plans to release his 2011 tax returns Thursday, NBC News reported. He said the documents will show he paid 31 percent of his income last year in taxes.
While Romney has declined to release his returns, he said he paid about 15 percent last year. Most of his income comes from investments, which are taxed at a lower rate than earned income.
The former Massachusetts governor has said he will release his return in April if he has the Republican presidential nomination locked in by then.
Gingrich spoke to a crowd of about 150 people in Winnsboro, S.C.
"We are going to name our flat tax the Mitt Romney 15 percent flat tax," Gingrich said. "My goal is not to raise Mitt Romney's taxes, but to let everyone pay Romney's rate."
Romney, who finished in the Iowa caucuses only a few votes ahead of former Sen. Rick Santorum, R-Pa., and won handily in New Hampshire, continues to lead in the polls for Saturday's Republican primary. Gingrich is trying to convince conservative voters to pick him as the alternative.