The actor and one-time "Saturday Night Live" TV star, who describes himself as a lifelong Democrat, told CNN that "young, very concerned New Jersey citizens" suggested the idea to him.
Piscopo, 53, declined to identify those who approached him, saying Friday that they wished to remain "in the background." He made no reference to whether he would run in a gubernatorial race.
A telephone message left by The Associated Press with Garden State Entertainment, a contact agency listed on Piscopo's Web site, was not returned.
McGreevey stunned the nation with his announcement that he is gay and had an extramarital affair with another man, whom sources in his administration identified as a former aide.
McGreevey said he would resign effective Nov. 15, touching off a tug-of-war between the lame-duck governor and factions on both sides of the political divide who demanded he step down immediately so a special election could be held to replace him.
"I don't mind him on a personal level hanging in until November, because he's got to do what he's got to do," said Piscopo, who counts McGreevey among his friends.