Leppert, speaking at the end of a city council meeting, didn't address his future, saying the meeting wasn't the "right forum." However, he said he expects to make an announcement "in the next several days."
The Republican has been mentioned as a possible candidate to replace Hutchison, who said last month she will leave the Senate after 19 years in 2012.
Republican Lt. Gov. David Dewhurst has said he's considering running for Hutchison's seat, and he likely would be the early favorite to win the party's nomination, the state's political experts have said.
Leppert's decision, which takes effect on Friday, means he will leave his job four months before the end of his first term. He previously announced he wouldn't seek a second term.
The Dallas city charter bars members of the city council from running for other offices while serving. A new mayor will be elected on May 14.
In his four years as mayor, Leppert added hundreds of police officers, promoted economic development and pushed through ethics reforms. However, he also lost several tough battles, including an attempt to limit Dallas' tax rate.
Leppert, his voice shaking, said he tried to move past the racial division that has often plagued the city of 1.3 million.
"I believe I'm leaving this city a better place than when I started," he said.
Mayor Pro Tem Dwaine Caraway will be interim mayor, putting him at the city's helm just weeks after he was embroiled in controversy over awarding a key to the city to Philadelphia Eagles quarterback Michael Vick.
Leppert later said the city didn't sanction the gift to Vick, who spent 18 months in prison for running a dogfighting operation.
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