Friedman and Maddon worked together for nine seasons with the Rays, with four playoff trips and one World Series appearance. While Friedman worked without a contract, Maddon's contract with the Rays extends through 2015.
Friedman plans for now to retain Dodgers Manager Don Mattingly for the 2015 season, according to a person familiar with the team's strategy but not authorized to discuss it.
That could leave Maddon -- a onetime Angels coach who keeps an off-season home in Long Beach -- as an option to manage the Dodgers in 2016. However, Maddon said Tuesday that he expects to discuss a contract extension with the Rays this winter.
"I want to continue to be a Ray, absolutely," Maddon said. "They have to want me to be a Ray too."
Maddon said he and his wife recently moved into a Tampa home once owned by former USC and Tampa Bay Buccaneers Coach John McKay.
"I'm really embedded here pretty well," he said. "The roots are pretty strong. We have a great infrastructure here. We have a great operation. We have great people.
"There's so much to like. There's only one negative. That's the ballpark. It's a big negative. But that's about it."
Maddon said the 37-year-old Friedman called Sunday to say he was unsure about the Dodgers job, then called again Tuesday to say he was taking it.
"He's off-the-charts bright," Maddon said. "He delegates well. He does not shy away from a difficult conversation. He's one of the best evaluators I've ever met, and I don't care what the birth certificate says. He's very dedicated to scouting and player development.
"There is nothing he doesn't do well."
Maddon said the Dodgers would be able to afford to apply all the analysis that the Rays sometimes could not.
"You'll have all the advanced thinking in the game," Maddon said, "all the metrics, all the data. You'll be on the cutting edge of everything. You'll be able to afford any mind or any machine, to create whatever edge you can."