Moseley-Braun, a Democrat who represented Illinois, told the Chicago Sun-Times the calls began coming in as soon as Mayor Richard Daley announced Tuesday he would not seek another term. In fact, she got a text message while the mayor was still speaking.
She said she is "seriously considering" becoming a candidate.
"This is all very new," she said. "I've been out of politics for a long time."
If she runs next year and wins, Moseley-Braun would be the second woman and the second black mayor in Chicago history.
The Daley family has had a near lock on the mayor's office for more than half a century. Richard J. Daley was mayor from 1955 until his death in 1976, and his son was first elected in 1989.
Moseley-Braun now lives in the Hyde Park neighborhood of Chicago and runs an organic food company. She served one term in the Senate from 1993 to 1999 and then as ambassador to New Zealand until 2001.