Updated at 1:26 p.m. ET

A new report suggests House Budget Chairman Paul Ryan, R-Wis., is "strongly considering" running for president next year.

The Weekly Standard, citing an unnamed Wisconsin Republican, reports that Ryan is "open" to running because "he is determined to have the 2012 election be about big things." Another unnamed source close to Ryan says in the conservative magazine's blog that the congressman is "coming around."

"While grateful for the continued support and encouragement, Congressman Ryan has not changed his mind," Ryan spokesman Kevin Seifert said in an e-mail to USA TODAY.

Ryan is widely respected in the GOP and is architect of a budget plan that would overhaul Medicare and cut federal spending $6.2 trillion over 10 years. The House passed the Ryan budget in April, but it died in the Democratic-controlled Senate.

The GOP budget -- and Ryan -- were chief targets in the House Democrats' campaign to support Kathy Hochul in a special House election in New York.

Ryan's name has come up occasionally as a possible presidential candidate, but the seven-term lawmaker usually has pushed back on such talk. This month on Fox News, Ryan said "no" to a 2012 bid.

GOP political strategist Karl Rove said last night on Fox that he believes Ryan and New Jersey Gov. Chris Christie, who has been emphatic about not running for president next year, are rethinking whether to join the race.