Sources told the New York Post's Page Six Nordegren, 33, and Cline, 53, have been dating since the holidays.
Cline, along with Harvey Weinstein, Groupon co-founder Eric Lefkofsky and Buffalo Sabres owner Terry Pegula, was the target of an attempted extortion plot last year when an aspiring actor threatened his family unless he forked over millions.
Cline, who has been married twice and has four children, hosted a fundraiser for Republican presidential candidate Mitt Romney at his home in September.
Nordegren was most recently spotted at the WGC-Cadillac Championship, at which Woods picked up his 76th PGA tour win.
The golfer is reportedly dating Olympic skier Lindsey Vonn.