As commissioner, Mr. Rettig would oversee the audit of Mr. Trump’s personal tax returns. The president has in the past said he would only release the returns once they were no longer under audit.

Writing for Forbes in 2016, Mr. Rettig said he would not advise Mr. Trump, then a candidate, to release his tax returns while an audit was continuing. “Is there any legal impediment to Trump publicly releasing his tax returns? Absolutely not,” Mr. Rettig wrote. “Would any experienced tax lawyer representing Trump in an I.R.S. audit advise him to publicly release his tax returns during the audit? Absolutely not.”

Mr. Rettig went on to speculate that Mr. Trump’s returns “might actually be somewhat unremarkable but for the fact they are the returns of Donald Trump,” and that it was “unlikely an accurate overall financial picture will surface by simply reviewing his returns. He likely pays taxes at a lesser rate than many of us given the nature of his real estate and similar investments being subjected to lower tax rates than salaries earned by the rest of us.”

Mr. Rettig also mused whether Mr. Trump might be inflating his wealth. “He is likely worth far more than us,” Mr. Rettig wrote, “but may be worth far less than the approximately $10 billion he wants us to believe.”

Mr. Rettig has deep experience with disputes over the amount of taxes paid. He has defended clients against the I.R.S. in tax fraud investigations. He has twice led negotiations that resulted in settlements between the I.R.S. and Americans who had been improperly sheltering money overseas.