Federal Reserve officials have agreed to sell some of the central bank's $1.1 trillion portfolio of mortgage-backed securities, but many are undecided on how soon or how aggressively to do so, the Wall Street Journal said, citing several people familiar with the matter.

Many Fed officials want to sell the securities after the central bank begins to raise short-term interest rates and tighten financial conditions, as the sale could push down prices of the securities and push up mortgage borrowing costs, the Journal said.

Richmond Fed President Jeffrey Lacker said earlier this week that the Federal Reserve should consider selling some of the mortgage debt it acquired during the financial crisis before raising interest rates, and added that he is worried about persistently high inflation expectations.

Last month, the Fed took steps to create tightening tools aimed at ensuring that inflation does not take hold once economic recovery gathers steam and renewed its pledge to keep benchmark interest rates extraordinarily low for an extended period.

Starting the selling process could take as long as a year or more and some officials have raised concerns that the sovereign debt crisis in Greece could have a spillover effect in U.S. markets, the Journal added.

Federal Reserve data on Thursday showed the central bank's holdings of mortgage-backed securities backed by housing finance companies Fannie Mae and Freddie Mac were $1.097 trillion as of May 5, up slightly from $1.096 trillion the previous week.

Officials at the Federal Reserve could not be reached immediately for comment by Reuters.

(Reporting by Anuradha Ramanathan in Bangalore, Editing by Chizu Nomiyama)