Bradley Tusk, a onetime political operative for Mr. Bloomberg, has embarked on a push to defeat Mr. de Blasio next year. He hopes to recruit a viable candidate, whom he would support with a barrage of positive ads as well as negative ads aimed at the mayor.

“The search for that mythical person continues,” Mr. Tusk said. “I don’t know if we’ll find that person or not.”

Mr. Tusk said he thought the ideal person to fill the role would be a Democrat able to take votes from Mr. de Blasio’s base while also appealing to more conservative New Yorkers, including independents and Republicans. That, he said, could be a Democratic politician or a wealthy businessman in the mold of Mr. Bloomberg.

The most likely course, Mr. Tusk said, would be for such a candidate to challenge the mayor in a primary. A strong but unsuccessful showing there, he said, could set up a third-party run in the November election.

Such a campaign could be made with an existing party, like the Women’s Equality Party or the Independence Party. Or a candidate could create a new party and secure a place on the ballot through a petition drive — a step that would need to be taken before the primary to have the ballot line in place as a fallback.

“The other route is skip the Democratic primary and just run in the general and you try to make that the Democratic primary, effectively, with a bigger electorate,” Mr. Tusk said, adding that he thought that route was unlikely.

He acknowledged that there were numerous obstacles to his plan, including the reluctance of many Democrats to vote outside their party, even for a candidate with strong Democratic credentials who had chosen to run on a third-party line.