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 KerryCongress needs to assert the war power against a dangerous president Sinclair and 'Big Media': The outrage that caused the outrage Tillerson sets a lost State Department on the right course 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 MarkeyEd MarkeySenate Dem: Trump has to stop ‘reckless’ language on North Korea Trump sparks debate over war resolution for North Korea Foreign Relations Dem: North Korea is the modern-day Cuban missile crisis 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.