Frank, 73, who served in the House of Representatives from 1981 until his term ended this week, said on MSNBC he has told Massachusetts Gov. Deval Patrick he would like to be part of the debate on federal fiscal policy following congressional passage of legislation preserving income tax rates for all but the wealthiest 2 percent of U.S. taxpayers.
He said the "deal now means that February, March and April are going to be among the most important months" in U.S. fiscal policymaking.
Frank -- who most recently served as chairman of the House Committee on Financial Services -- had said in recent weeks he did not want to succeed Kerry in the Senate because it would be "kind of like you're about to graduate, and they said 'You gotta go to summer school.'"
He said Friday he wouldn't run in a special election scheduled for this summer to choose a longer-term successor to Kerry.
"It's only a three-month period; I wouldn't want to do anything more," he said. "I don't want to run again."
Others being mentioned as interim replacements include former Massachusetts Gov. Michael Dukakis and former Massachusetts Supreme Court Justice Margaret Marshall, the Boston Herald said Friday.
U.S. Rep. Ed Markey, D-Mass., has said he will be a candidate in the summer election.