The Daily Caller news website has close ties to the Cheney family, with co-founder Neil Patel having served as the former chief policy advisor to Vice President Cheney.
The source said Ms. Cheney is seriously considering running, according to The Daily Caller.
The conservative blog Hot Air was skeptical that she would challenge Republican incumbent Mike Enzi, should he confirm his own rumored run, but still hoped she's take "a shot at it."
Ms. Cheney, a lawyer by training, has developed her own political profile in recent years, said Britain's Daily Mail, listing her work with the State Department under former President George W. Bush and her involvement with the Republican-leaning non-profit organization Keep America Safe, which she co-founded.
The report comes amid growing speculation over a potential Cheney run, said The Washington Times.
According to The Daily Caller, even though Cheney has avoided a public statement on the issue, she "recently moved to Jackson Hole, Wyo., with her family" and "has also been giving speeches at various events in the state."