Paul has visited critical early primary states such as Iowa, South Carolina and New Hampshire, speaking and meeting with local Republican leaders, The Washington Post reported.
The trips went largely unnoticed because, until now, no one thought the newly minted senator would seriously consider the race.
"Rand would not run if his dad's running," said Jesse Benton, political director for Paul's father, Rep. Ron Paul, R-Texas. "But if his dad doesn't run and he fails to see a viable candidate or candidates in the Republican field, that are serious about debt spending and the budget crisis facing our country, then he will be very tempted to weigh his options."
Even though he raised impressive amounts of money online for his Senate bid, Paul does not have a large, national network of supporters or a huge fundraising capability as does Rep. Michele Bachmann, R-Minn., another potential dark horse presidential candidate.
Still, the similarities between Rand and Ron Paul may allow the son to assume much of his father's ardent following if the older Paul opts to run in 2012, the Post said.
Rand Paul, just as his father, isn't hesitant to break with mainstream Republican dogma. He has called for ending all aid to Israel and is against the intervention in Libya. He said he wants $500 billion in budget cuts -- way more than the GOP leadership proposed. He also was the lone "nay" vote on a measure that would make it a federal crime to direct a hand-held laser pointer at an aircraft.
Trader Joe's: Car crashes into Long Island store, injuring 11
Exploding whale video goes viral on Internet