July 28, 2016 9:07 p.m. ET

PHILADELPHIA—New York City Comptroller Scott Stringer and Bronx Borough President Ruben Diaz Jr. dined at one of Philadelphia’s steakhouses this week, having drinks as they discussed how they might try to unseat Mayor Bill de Blasio.

The two Democrats, both seen as potential challengers to Mr. de Blasio, also a Democrat, discussed various scenarios in which they might enter the 2017 primary as they dissected the mayor’s strengths and weaknesses, a person familiar with the matter said.

While there was plenty of talk about the 2016 race for the White House at the Democratic National Convention, there was ample speculation at late-night political parties about whether Mr. de Blasio could be defeated next year—and who could do it.

“Everyone I sit with or pass by casually brings up 2017,” said Mr. Diaz, who would be the city’s first Latino mayor if he ran and won. “It seems like that’s on everyone’s lips.”

 Bronx Borough President Ruben Diaz Jr. 

Bronx Borough President Ruben Diaz Jr. 

Even with Mr. de Blasio’s lagging approval rating and various investigations into his administration and fundraising activities, he remains a formidable candidate for re-election. An aide to the mayor didn’t respond to a request for comment.

Mr. de Blasio, 55 years old, holds deep institutional labor support. His approval rating in the black community remains about 60%. And as the incumbent, he will be able to raise significant sums of money.

It isn’t clear if any formidable challengers will jump into the race.

While several probes involving the mayor are ongoing, neither Mr. de Blasio nor his closest aides have been accused of any wrongdoing.

For Mr. de Blasio, who became the city’s first Democratic mayor in 20 years when he took office in 2014, the notion that he could face a significant primary opponent is a clear sign that fellow Democrats think he is politically vulnerable.

 Stringer and DeBlasio

Stringer and DeBlasio

Mr. Stringer, who planned to make a bid for mayor in 2013 but ended up running for comptroller, dined this week with Michael Mulgrew, president of the United Federation of Teachers, and Charlie King, a political consultant with close ties to New York Gov.Andrew Cuomo, whose relationship with Mr. de Blasio is acrimonious.

Mr. Stringer has held other meetings in which 2017 has come up, a person familiar with the matter said.

“We as Democrats need to focus on ’16 ahead of ’17,” Mr. Stringer said, playing down the meetings.

Mr. Diaz said he met with a number of potential donors and others during the week. He confirmed the steakhouse meeting with Mr. Stringer and said they “absolutely” discussed 2017, though he declined to comment on the details of the conversation.

Mr. Stringer has signaled to allies that he is serious about a run for mayor next year and is considered by many consultants to be the most likely to enter the race. He has told people he believes Mr. de Blasio is damaged and wants to be ready, people familiar with the matter said.

Mr. Diaz said he hasn’t decided whether he will run for re-election or for mayor and will continue to evaluate the landscape. He said he didn’t know if Mr. Stringer would enter the race, but Mr. Stringer’s decision would have an impact on his plans.

U.S. Rep. Hakeem Jeffries, a Democrat who represents parts of Brooklyn and Queens, was frequently spotted in the Loews Hotel lobby, chatting with New York political operatives and legislators.

“I haven’t completely ruled it out—running for mayor,” Mr. Jeffries said.

Political consultants at the convention were buzzing about a poll that examined potential matchups between Mr. de Blasio and Mr. Stringer, as well as Mr. de Blasio and Christine Quinn, a former City Council speaker. It wasn’t clear who commissioned the poll.

Among those getting attention was Ms. Quinn, who ran unsuccessfully for mayor in 2013; she now is an executive at an agency helping the homeless.

Ms. Quinn traveled around Philadelphia with political consultants, frequently appeared on television and attended several lunches and parties, greeting strangers and friends alike with a kiss and an audible “mwah!”

Ms. Quinn said she had no plans to run for mayor in 2017.

“Do I hope to someday run for office again? Sure,” she said. “I love this, the games and all the people.”

The former speaker has made an effort to build her profile over the past year, appearing on CNN, talking publicly about her homeless residents and serving as vice chairwoman of the state’s Democratic Party.

With her booming laugh, Ms. Quinn dismissed all the talk about her challenging Mr. de Blasio.

“People thought I was going to win last time,” she said. “If people’s thoughts were true, there would have been a different mayor.”

 Cuomo and DeBlasio haven't seen eye to eye

Cuomo and DeBlasio haven't seen eye to eye