But neither the mayor nor the senator, both Democrats, broached the issue when they passed each other Tuesday in a Capitol hallway in Harrisburg. They hugged and exchanged pleasantries, Williams said. But that was all.
The senator said he isn't sure yet if he's in or out, and won't yet say when he'll make that decision - except that it won't be quite as late as 13 weeks before Election Day, when he decided to run for governor.
"Are people talking to me about it, and aggressively? Yes," Williams said. "Am I listening to them? Yes, I am."
The Nutter campaign is not sitting idly by. On Thursday morning, the mayor was expected to announce that a key Williams ally and top Philadelphia official - District Attorney Seth Williams - is backing him for reelection.
The endorsement follows another early campaign announcement just before Christmas, that Philadelphia's three local members of Congress - Bob Brady, Chaka Fattah, and Allyson Schwartz - were all lining up behind the mayor.
"If there are interested competitors who are trying to gauge how strong a candidate he is, I think these endorsements show that," Nutter campaign spokeswoman Sheila Simmons said. "And they can interpret them as they like."
Though Nutter has been criticized in political circles for struggling to move his agenda forward, many political observers now anticipate the race in the end will be a sleeper, with no eventual primary challenger emerging - especially given the mayor's head start in fund-raising and city rules that cap campaign donations. Besides, no Philadelphia mayor who has sought reelection has lost.
Anthony Williams, who has an amicable relationship with Nutter, is undeterred. "There are other ways to be competitive," he said, declining to explain.
The presence in the primary of Anthony Williams, who like Nutter is African American, could open the door for a third candidate - likely white - looking to take advantage of a split in the black vote.
After his race for governor - Williams came in third in a four-way primary race - he said he would run for state auditor general in 2012, and would not challenge Nutter.
"This man is my friend. This man endorsed me," he said at the time, adding that he would campaign so hard for the mayor that he would "pull you out of your house to vote for him."
In an interview Wednesday, Anthony Williams said he was reconsidering because of a leadership semi-void described to him by city and regional leaders. He would not identify them, but said many told him Nutter was not decisive enough and had failed to effectively communicate his administration's central message.
"Michael Nutter is more policy than politics," he said. "And I think Philadelphia requires both."
Nutter, however, has a record of surpassing political expectations - namely, his victory in the 2007 five-way Democratic primary, which featured two well-known congressmen, a veteran state representative, and a millionaire. Nutter also out-raised them all.
In that vein, Thursday's endorsement by Seth Williams is illustrative of the mayor's methodical and strategic ways. Anthony Williams has been one of Seth Williams' chief supporters, and was among the first at the microphone to praise him at his 2009 primary victory party.
At the same time, Nutter at the eleventh hour endorsed a rival to Seth Williams in that race, placing prerecorded robo-calls for Dan McElhatton.
Seth Williams did not return a call Wednesday to talk about his expected endorsement.
Of Seth Williams' backing, Simmons said: "We are very pleased to have some very respected leaders in our community coming out to say they support the mayor, and giving him a vote of confidence for the next term."
While the campaign has yet to hire a campaign manager, it has retained the same pollster - Peter D. Hart Research Associates - and media consulting firm - the Campaign Group - hired by Nutter in 2007.
It has also leased space in the same Center City building, but on a different floor.
"We're in Suite 1313," Simmons said. Asked about that unlucky number, she said: "We're not afraid."
Contact staff writer Marcia Gelbart
at 215-854-2338 or firstname.lastname@example.org.
Inquirer staff reporter Jeff Shields contributed to this article.