Monti said on Friday he wanted his alliance to go beyond traditional political boundaries and unite a coalition of factions and civil society groups around a reform agenda aimed at tackling Italy's economic woes.
His announcement ended weeks of speculation over whether he would run for a second term and pits him against Bersani's centre-left Democratic Party (PD) and Silvio Berlusconi's People of Freedom (PDL) group.
But Bersani urged the former European Commissioner on Sunday to be clearer about whether he supports a left or right-leaning agenda and outline the choices he would make on issues such as civil rights.
"This centrist alliance needs to explain exactly where they stand," Bersani told reporters on Sunday. "Does Monti and the centre not think that the bipolar political system is working? Do they want to dismantle it? If not, then which side are they on?"
He repeated that the centre left would be open to discussing a possible alliance with Monti once his position was clearer.
Bersani's demands come after Berlusconi attacked Monti on Saturday, accusing him of striking a hidden deal with the left to help them secure power after the February 24-25 elections.
Pier Ferdinando Casini, head of Italy's oldest and largest centrist party, the UDC, which is backing Monti, has denied that any secret accord has been struck and quickly rebuffed Bersani's demands.
"The PD does not want a competitive and uncomfortable centrist grouping because they prefer the old and eternal fight with Berlusconi," he said.
Monti was appointed to head a technocrat government last year to save Italy from financial crisis after Berlusconi stepped down as prime minister. While Monti has won the backing of investors, the business community and the Catholic Church, many Italians have become increasingly tired of the tax hikes and spending cuts he has imposed to shore up battered public finances.
Opinion polls suggest the PD will win a comfortable lower house majority but may have to agree a deal with centrist forces in the Senate, where the centre left has struggled to gain control in past elections.