The election hasn’t even been scheduled, and may never happen.

But in an indication of the suddenly shifting terrain of Massachusetts politics, Democratic candidates are lining up to run for Edward J. Markey’s House seat, should the veteran Malden represenative win the special election for US Senate.

The early rush could be for naught: If Markey loses his Senate race, he will return to the House seat he has held for more than 36 years, and no election will be held.

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But the dash is on among those who have their eyes on a rare shot at a Congressional seat in Massachusetts.

State Representative Carl Sciortino of Somerville said last week—in the midst of the blizzard—that he has launched a campaign for Markey’s seat.

First elected to the state House in 2004, Sciortino has been a leading supporter of gay rights, and coauthored a transgender rights bill that was signed into law last year.

State Senator Katherine Clark of Melrose is planning to launch her own campaign for Markey’s seat on Friday, according to people who have spoken to her. First elected to the Legislature in 2008, Clark is a former school committee member and prosecutor.

State Senator William Brownsberger of Belmont is campaigning for the seat as well. A former prosecutor and defense attorney, he said he launched his federal campaign committee last week.

“I love being in the Senate, and I’m enjoying my job, but this is an opportunity that only comes around once in my political lifetime,” Brownsberger said. “I’m 100 percent in the race, on the assumption Ed Markey wins.”

Brownsberger said an election could be scheduled this fall, if Markey wins.

Other Democrats who have been mentioned as possible candidates include State Senator Karen Spilka of Ashland, Peter Koutoujian, the Middlesex sheriff, and state Representative David Linsky of Natick.

A long list of Democrats are also said to be looking at US Representative Stephen F. Lynch’s seat, though none have officially declared. Lynch, of South Boston, is challenging Markey for the Democratic Senate nomination. The primary is April 30.

The potential candidates for his seat include state Representative Martin Walsh of Dorchester, City Councilor Rob Consalvo of Hyde Park, former City Councilor Michael Flaherty of South Boston, State Senator John Keenan of Quincy, Mayors Thomas Koch of Quincy, Joseph Sullivan of Braintree, and Susan Kay of Weymouth, as well as former mayor Jack Yunits of Brockton.