Three or four Massachusetts lawmakers may look at running for the vacant seat in their state, but many will be discouraged because of plum House positions, Rep. Barney Frank (D-Mass.) said Thursday.

"Frankly, in 2004, most of us were thinking about running when John KerryJohn Forbes KerryJohn Kerry’s memoir title revealed GOP senator: Democratic opposition to Pompeo 'driven 100 percent by politics' North Korea is moved by Pompeo diplomacy, but Dems dig in deeper MORE looked like he might become president, because we were in the minority," Frank said in a telephone interview on MSNBC. "And when you're in the minority, you don't have much of an impact."

Frank backed the idea of an interim senator to replace the late Sen. Edward Kennedy (D-Mass.) before a special election could be held, but said it would be a mistake for some lawmakers to give up high-ranking positions in the House.

But the veteran House member, the chairman of the House Financial Services Committee, seemed to take himself -- and others -- out of consideration for the Senate seat.

"I've got a committee chairmanship that's very important to me and to the things I'm trying to do," Frank said, naming Reps. Ed MarkeyEdward (Ed) John MarkeyDem senators demand Trump explain ties to Koch brothers Overnight Cybersecurity: Senators want info on 'stingray' surveillance in DC | Bills to secure energy infrastructure advance | GOP lawmaker offers cyber deterrence bill Overnight Tech: Alleged robocall kingpin testifies before Congress | What lawmakers learned | Push for new robocall rules | Facebook changes privacy settings ahead of new data law | Time Warner CEO defends AT&T merger at trial MORE (D) and Jim McGovern (D) as others with important positions.

"I think three or four may run, but I think many of us have positions now that it would be a mistake to give up," he added.

Frank praised the late senator, but noted that his voice had been absent for some months now in the Senate, as Kennedy had been holed up in Massachusetts during his struggle against cancer.