The GOP has sought new opportunities to pick up seats and cut into the Democratic majority on Capitol Hill after Republican Scott Brown's recent upset in a special Senate election in Massachusetts.
Coats brings a high profile to the race, where Republicans believe the two-term incumbent may be vulnerable.
It was in 1998 when Coats decided not to seek re-election, avoiding a race with then-Gov. Bayh. Since then, Coats has served as ambassador to Germany under President George W. Bush and worked as a lobbyist in Washington.
The GOP officials spoke on condition of anonymity because Coats hasn't announced his intentions.
Republicans intend to make an issue of Bayh's support of President Barack Obama's agenda, including health care legislation and the economic stimulus.
In a statement to Howey Politics, a political news Web site in Indiana, Coats said he was re-entering politics because he is "increasingly alarmed and frustrated about the direction of our country and by a failure of leaders to listen to those they were elected to represent."
The deadline to file for the race is Feb. 19.
Coats is a conservative Republican, while Bayh is a moderate Democrat who toyed with the idea of running for president in 2008.
When Coats retired in 1998, he said he was tired of constantly raising money to run for office. Bayh went on to defeat the mayor of Fort Wayne, Ind., and won re-election comfortably in 2004, even as President George W. Bush captured a second term.
Democrats are likely to make an issue of Coats' work in the private sector, which has included lobbying for financial companies.