George Allen said yesterday that, contrary to reports out of Montreal Friday, he already has purchased 20 percent of that city's professional football team, with an option to buy 31 percent more by Dec. 31.

Allen, who Friday was named president and chief operating officer of the Montreal Alouettes of the Canadian Football League, would not say how much he paid owner Nelson Skalbania, but Montreal sources have placed the investment in the $600,000-to-$700,000 range. Neither Skalbania nor league officials were available for confirmation.

In a telephone interview from his California home, the former Redskin coach also said:

He eventually will be the team's coach, although possibly not this year. He refused to be more specific about when he would coach the team.

He might be interested in Redskin quarterback Joe Theismann and he might consider former Redskin Billy Kilmer for an assistant coaching job.

If he decides "I can't turn things around up there" and no longer wants to own part of the team, he can exchange his present 20 percent ownership for a lump sum of money by Dec. 31. He would not say what that sum would be.

If he purchases the additional 31 percent by Dec. 31 to become the majority owner, he then has an option to buy the remainder of the team by Dec. 31, 1983.

He is putting together a group of investors, both individual and corporate, to help finance his future dealings with the Alouettes. But he maintained he had purchased the first 20 percent on his own.

He has been assured by Skalbania--and Skalbania has told the league--that the Alouettes will pay off their outstanding debts by March 1. Allen said those debts "are about $1.2 million." They previously had been reported as $1.4 million.

He has learned that quarterback Vince Ferragamo has a personal services contract with Skalbania. Allen said that Skalbania is responsible for the remaining three years of Ferragamo's $1.35 million contract, not the Alouettes.

In reply to questions about his coaching plans and about Theismann, Allen said: " . . . right now decisions about quarterbacks and coaches are secondary. We have to concentrate on getting the Alouettes on a sound financial basis. I think this franchise has an unlimited future. It's an unlimited opportunity, and I can make out of it what I want."

Allen admitted that his decision to move to the Canadian Football League after four years of football exile in California came in part out of frustration from seeking another coaching job in the NFL.

"I had an NFL owner fly out here to see me two years ago and I could have had that job, I think, if I wanted it," said Allen, who would not identify the owner. "But chances are, with the type of person I am, that it would have been difficult for me to get what I wanted in the NFL. It would have been difficult for me to compromise. I have to be myself.

"I had a couple of assistant coaching jobs offered me and three college jobs and five clubs in the new league (United States Football League) made some very tempting offers, but this one with Montreal was the best because I could be an owner.

"I've already rebuilt two franchises (Los Angeles and Washington) and they are worth $44 million each. Now I have a chance to do the same thing again and we can benefit from it directly for a change."

Skalbania bought the Alouettes for $7.5 million last year, which is slightly more than NFL teams receive in television revenue alone this year. But Allen said he thinks the value of the Alouettes "is almost limitless" because of cable television possibilities "if we can turn it around and make it appealing, and that's what we are going to do."

Montreal long has been considered potentially the most lucrative franchise in the CFL because of the city's large population base and 60,000-seat stadium. But Allen says that although the Alouettes have "a lot of (U.S.) players under big contracts, they haven't done very well with Canadian players. That's where I am going to concentrate."

He indicated that he would not try to keep high priced linebacker Tom Cousineau, who is seeking a $600,000 contract next season, probably in the NFL. But he said he wasn't sure what he would do about Theismann, who is a Redskin free agent.

"Joe would be a big hit," Allen said. "He's ideal for the league, mobile with a quick release. And he's been here before (Toronto). But with Vince still here and a good Canadian quarterback (Bill Johnson), quarterback isn't a big priority."

Asked if he would hire any of his former players as assistant coaches, Allen volunteered that Kilmer "would make a heck of a quarterback coach, although we need assistants who are familiar with the Canadian game.

"I also don't know if I will coach or not this year. I'll coach eventually, but when is the question. I've got a lot of things to do first. I have some exciting ideas for promotions but I can't talk about them until the league approves them. But we need to get things rolling. I already like the team colors (red, white and blue) and the city is terrific, clean and no crime. It's one of the best 10 cities in the world."