George Allen, the former Washington Redskin coach who has been out of professional football since 1978, was hired yesterday as head of football operations for the beleaguered Montreal Alouettes of the Canadian Football League, according to owner Nelson Skalbania, who said he also has agreed to sell Allen 51 percent interest in the team.

Skalbania, who bought the team for $7.5 million last April, told a Montreal radio station that Allen has agreed to purchase a majority interest, but a league spokesman said the CFL had not received an ownership application from Allen. The Alouettes lost more than $4 million in 1981 and are now $1.4 million in debt.

"The CFL should be grateful that Mr. Allen has agreed to come to Montreal," said Skalbania yesterday. "Nobody in Canada was willing to gamble on the franchise." It appears Allen will not coach the team; his official titles will be announced today.

Jake Gaudaur, the CFL commissioner, said Skalbania had brought Allen in to allay the league's fears that the Alouettes would not be financially stable in 1982.

"Nelson Skalbania has named George Allen as the senior on-site manager of the club," Gaudaur said. "His titles you will have to ask him about."

Before Allen can purchase any part of the Alouettes, he must be approved both by the league and by the Canadian Foreign Investment Review Agency, which is responsible for ruling on whether new foreign investment is beneficial to the country. No American has been accepted as a CFL investor, according to league officials.

Seven of the league's nine teams must approve any ownership change. According to league sources, such approval could take place in this case within two to three weeks.

Allen, who met with Skalbania in Toronto yesterday, was not available for comment. His specific duties with the Alouettes apparently will be detailed today at a press conference in Montreal, but he probably will be named president and possibly general manager.

Skalbania currently is being quizzed by the league on the status of the Alouette franchise. Skalbania told the league yesterday he still owes former owner Sam Berger $750,000 of the original purchase price. Under the CFL constitution, the team could be taken away from Skalbania if it is found his operations are detrimental to the league.

Allen and Skalbania first talked last March about Allen's possible role as a part owner, even though the CFL had not approved Skalbania's purchase. Allen soon removed himself from consideration, however.

Since being fired by the Los Angeles midway through the Rams' 1978 training camp, Allen has been seeking another National Football League coaching position. He has contended he is being blackballed by NFL owners, who are unwilling to turn over control of their team to Allen.

Allen had a 120-54-5 record in the NFL, but was fired twice by the Rams and once by the Redskins. During his seven years in Washington, Allen took the Redskins to the playoffs five times, including their only Super Bowl appearance. He was released on Jan. 18, 1978 by team president Edward Bennett Williams after refusing to sign a new contract with the team.

Allen will be taking over a chaotic situation at Montreal, brought about by Skalbania's flamboyant attempts last year to transform the Alouettes into a playoff contender with his checkbook.

Skalbania signed Vince Ferragamo, the Ram quarterback, and wide receivers James Scott (Chicago) and Billy (White Shoes) Johnson (Houston), and two highly touted rookies, Keith Gary (drafted by Pittsburgh) and David Overstreet (drafted by Miami). He gave Ferragamo a guaranteed four-year contract calling for $450,000 a year. Ferragamo eventually was benched and did not play the last two games of the 3-13 season.

Skalbania already has fired coach Joe Scannella and his chief operating officer, Bob Geary, along with most of the remaining front office personnel.

"Nelson has showed he has reduced his indebtedness but it seems to us there is substantial indebtedness yet," said Gaudaur. "But it also seems to us that it can be eliminated. I think with the serious management of George Allen that will be accomplished."

Skalbania said he sought Allen's financial assistance after several offers from Canadians fell through.