A rising star in Albany political circles, one who also has gained national prominence, is quietly entering the ranks of potential candidates for mayor in 2009.

Political sources say they are hearing Attorney General Andrew Cuomo’s name in connection with a mayoral run, and they argue that he shouldn’t be discounted as a candidate to replace Mayor Bloomberg. It may be that Mr. Cuomo sees an opening in the Democratic mayoral field, as New Yorkers cast about for new candidates to join the race and the leading Democratic contenders struggle to excite voters.

One criticism of those who have demonstrated interest in the office is that none have the credentials that Mayors Bloomberg and Giuliani brought to City Hall, a complaint that would not apply to Mr. Cuomo, the state’s top lawyer and a member of President Clinton’s Cabinet.

Mr. Cuomo could find City Hall an appealing destination as he tries to imagine his political future in Albany, which appears to have hit at least one roadblock. Although he was considered a potential challenger to Governor Spitzer, with whom he had an often-tense relationship, it is widely believed that he would not challenge Mr. Paterson in a Democratic primary for governor in 2010. A run for a Senate seat also seems unlikely, now that Senator Clinton has lost the Democratic primary.

In running for mayor, Mr. Cuomo, an ambitious politician who lives in Manhattan and was born in Queens, would be following in his father’s footsteps. Governor Cuomo ran for mayor in 1977, losing to Mayor Koch.

A spokesman for Mr. Cuomo, John Milgrim, didn’t rule out the possibility of a mayoral run, saying only that Mr. Cuomo “is completely focused on being the best attorney general possible.”

Since being elected attorney general in 2006, Mr. Cuomo has racked up a string of victories for his office, including an announcement yesterday that three major Internet service providers, Verizon, Time Warner Cable, and Sprint, had agreed to block access to child pornography displayed online.

In 2007, an investigation by his office into the relationship between universities and lenders led to a settlement with several universities and a payout of $3.27 million to students. Citibank also agreed to follow a code of conduct established by the attorney general’s office, and put $2 million into a fund designated for education programs to teach students and parents about the student loan industry. Last year, he got the social networking site Facebook to agree to safeguards to protect users from sexual predators as part of a settlement following an investigation.

At a fund-raiser for Mr. Cuomo held in January, Mr. Bloomberg called the attorney general “the people’s lawyer,” a source said, praising him for his work on gun control, Medicaid fraud, student loans, and the environment.

His reputation is apparent in his polling numbers. In an April poll by Quinnipiac University, 62% of New York City voters said they approve of the way Mr. Cuomo is handling his job at attorney general. He won a 65% approval rating from voters statewide.

A likely mayoral candidate, Christine Quinn, the City Council speaker, received an approval rating of 43% from city voters in a Quinnipiac poll in May. Comptroller William Thompson Jr., another mayoral candidate, won approval of 51% of voters surveyed.

A former aide to Mr. Bloomberg and governors Cuomo and Carey, William Cunningham, said that although he hasn’t seen any evidence Mr. Cuomo is interested in the job, he should be.

“He has a lot of resume bases covered, so it would be interesting,” Mr. Cunningham said.

Mr. Cuomo’s career wouldn’t be taking a step back if he ran for mayor. Messrs. Bloomberg and Giuliani have raised the profile of City Hall, using the mayoralty to enter national politics, the latter as a Republican presidential candidate and the former as a much-speculated potential candidate for the White House.

Governor Cuomo told The New York Sun that his son would make a good mayor — as well as a good governor and president.

“Whatever he does, he does well. Just look at what he did at HUD,” he said, referring to Mr. Cuomo’s time as secretary of Housing and Urban Development in the Clinton administration.

Mr. Cuomo said he hadn’t heard his son’s name floated as a potential mayoral candidate, and said he didn’t have any opinion about whether his son should run for mayor.

“You should ask him,” he said.

A spokesman for Mr. Cuomo did not make the attorney general available for an interview.