PHOENIX — The replacement for state Sen. Jake Flake who died Sunday could have a familiar name — at least for the near term.

 Rep. Bill Konopnicki, R-Safford, who represents the same Eastern Arizona district, said he understands that the family of the 11- year legislative veteran wants one of his brothers or children appointed to fill out his term which runs through the end of the year.

 “That would be a very nice tribute to Jake,’’ said Konopnicki.

 That decision rests with members of the Navajo County Board of Supervisors who now must appoint a committee to screen potential replacement and recommend three names.

 All of the nominees have to be Republicans, like Flake. And all need to be residents of Navajo County — disqualifying Konopnicki who is a Graham County resident — even though the legislative district encompasses all or part of seven counties.

 Board members must choose from the list, with a new senator expected to be named within two weeks.

 Flake’s death leaves the Republicans with a 16-13 edge in the Senate, even as lawmakers struggle to finish the current session.

 The main thing holding that up are negotiations to bridge what could be a $2.2 billion gap between anticipated revenues and expenses for the new fiscal year that begins July 1.

 Longer term, Konopnicki said he hopes to get a chance to succeed Flake after the November election. That, however, will require him to get the blessing of the GOP precinct committeemen and committeewomen from throughout the district.

 Flake, 72, collapsed at his home Sunday, two weeks after breaking eight ribs in a fall from a horse.

 The legislator already had filed the necessary nominating paper to run for a third term in the Senate. For all intents and purposes, he already was elected: No one else from either part had submitting the necessary petitions by last week’s deadline.

 Deputy Secretary of State Kevin Tyne said state law allows the Republican precinct workers in the legislative district to put a different name on the Sept. 9 primary ballot.

 Konopnicki, who already had submitted his signatures to seek reelection to the House, said Monday he will ask the party officials to put his name up for Flake’s senate seat.

 “At this point I’m hoping that I would be the only name they would consider,’’ he said.

 That move, in turn, would remove Konopnicki’s name from the House race for the district — and sets the process in motion again for party officials to name another candidate for the district’s two House seats.

 There already is another Republican on the ballot: Snowflake resident Sylvia Tenney Allen. Konopnicki said the name carries some political weight in the district as she is the aunt of Navajo County Supervisor David Tenney.

 The Democrats have only a single House candidate in the district for the two seats, incumbent Jack Brown of St. Johns. He represented the district in the House from 1963 through 1974 an was elected to the Senate in 1996, the same year Flake became a House member.

 In fact, Brown and Flake, who have cooperated on some issues despite their different political affiliations, essentially switched seats in the 2004 election when they reached the constitutionally mandated cap of eight consecutive years in the same office.

 Brown, however, said Monday he has no interest in trading a likely sure reelection to the House to run a contested race against Konopnicki for the Senate.

 He also noted that the process for any Democrat to get on the ballot for Flake’s senate seat is more cumbersome than it would be for a Republican. Because no Democrat submitted nominating papers, an individual would have to run in the Democrat primary as a write-in candidate.

 And Tyne said it would take more than that person voting for himself or herself. He said state law spells out that a Democrat in that district would have to get at least 385 people to write in the name, the same number of signatures that would be required on nominating papers.