Three of professional football's most popular and proficient quarterbacks were among seven finalists selected today for the Professional Football Hall of Fame voting.

Joe Namath, Roger Staubach and Fran Tarkenton joined running backs O.J. Simpson and Paul Hornung, NFL Commissioner Pete Rozelle and former Cleveland Browns center Frank Gatski on the final ballot.

It is possible all seven could be named to the Hall of Fame, which will announce the final choices Tuesday. The seven were picked today from an original list of 15 after two ballots of the Hall's selection board, made up of one media representative from each of the 28 NFL cities and one at-large member.

To gain entry into the Hall in Canton, Ohio, a finalist must be named on at least 24 of the 29 ballots. Six negative votes would eliminate the nominee. Voting was done by secret ballot and will be audited by an independent accounting firm.

Judging from sentiments expressed by the voting membership during a discussion of each man's qualifications, it seems all seven have an excellent chance of making the Hall.

Staubach and Simpson were on the ballot for the first time. The exclusion of Namath, Hornung and Tarkenton over the last few years has spurred considerable controversy. All three seemingly have impeccable credentials, as do the other finalists.

Namath did not play for many winning teams on the New York Jets in the late 1960s and early '70s, but he did win one game -- Super Bowl III against the Baltimore Colts -- that many believe gave credibility to the old American Football League during its merger with the NFL, which set off the tremendous growth of the game over the last two decades.

Staubach needs no introduction in Washington. In his nine years with the Cowboys, Dallas played in six NFC title games and won Super Bowls VI and XII. Staubach led the league in passing four times.

Tarkenton played 18 seasons in the NFL, 14 with the Vikings. In his last seven years, he led Minnesota to six Central Division titles and three NFC titles. The consummate scrambler, he holds NFL passing records for attempts (6,467), completions (3,686), yards (47,003) and touchdowns (342).

Simpson played on some of the worst teams in NFL history with the Buffalo Bills, yet managed to run for over 1,000 yards for five straight seasons, including 2,003 in 1973. He was the first runner to go over 2,000 yards and was a unanimous all-pro from 1972 to 1976.

Hornung was a mainstay on the great Green Bay Packers teams of the 1960s, an all-purpose back who also kicked. His coach, Vince Lombardi, once said Hornung was the best running back in football inside his opponent's 20.

Rozelle now is in his 25th year as commissioner, and although the NFL has had serious problems with declining television ratings, litigation over franchise shifts and a bidding war with the U.S. Football League, he is responsible for the game's continued high level of popularity, not to mention a landmark television contract that will earn his league $2.1 billion by the time it runs out in 1986.

Gatski was the choice of the Hall's Old Timers Committee, selecting from players who played before 1960. He spent 12 seasons at center and linebacker for the Cleveland Browns and Detroit Lions, and was in 11 championship games.

Among the 15 finalists eliminated today was one Washingtonian, defensive back Willie Wood of the Green Bay Packers, who made it to the cut to 10 players. Also on the original ballot were former Oakland coach John Madden, defensive linemen Carl Eller of Minnesota and Buck Buchanan of Kansas City, linebacker Willie Lanier of Kansas City, safety Johnny Robinson of Kansas City, and wide receivers Fred Biletnikoff of Oakland and Don Maynard of the Jets.