"AC Milan especially have really caught my eye, they cause a lot of problems for the opposition, they are strong in every part of the field and they are so good defensively with (Paolo) Maldini and Cafu playing as well as ever," said Beckham.
The England skipper was speaking to journalists on a visit to London to launch the David Beckham soccer Academy.
"Chelsea, though, are also a major contender. They have Roman Abramovich's money, a new young manager who is full of confidence and keeps the pressure off his team, some very, very good players maturing well, and some good young English players there. They will take some beating too."
The draw for the Champions League quarter-finals takes place on Friday at UEFA's headquarters in Nyon.
However, Beckham could hardly hide his frustration at Madrid's lack of success in Europe's leading club competition during almost two seasons at the Bernabeu.
Real were knocked out at the quarter-final stage last season and their 2-0 defeat at Juventus last Wednesday meant an exit in the round of 16 this time.
After losing 2-1 to Getafe on Sunday, Real are also 11 points behind Barcelona in La Liga with virtually no chance of catching their arch-rivals in the Spanish title race.
"Of course, it is incredibly frustrating because I want to win trophies with Real Madrid but, unless something happens to Barcelona's form, we won't win La Liga and we are out of Europe.
"A club like Real Madrid needs to win trophies but that is not going to happen this season. There may be a number of reasons why it has happened, we have to accept it, look at it, but I don't like it."
NO MANAGEMENT
Despite the lack of silverware at Real, the England captain confirmed he is happy at the club and has no intention of returning home for the foreseeable future. He is also certain about what he wants to do once his playing days are over.
"Well I know that I do not want to become a manager. I have no ambition to do that, that has never been a thing for me.
"Other players might. I think Gary and Phil Neville would make great managers and so would Roy Keane, he sets a great example, he's got experience, and that something extra," he said, referring to his former Manchester United team mates.
"But for me, I want to put something back into the game through the kids and I am delighted to be in a position to start the academy.
"I want to continue playing for as long as I can at the top level but when the time comes I want to coach the kids," said the 29-year-old.
"I am putting a lot of my own money into this project but its not necessarily about finding a new Michael Owen or Wayne Rooney or Rio Ferdinand, although that would be great if that did happen, but its not just about elite young players.
The David Beckham Academy will open this year in Greenwich on the banks of London's River Thames close to the site of the Millennium Dome and will initially welcome 15,000 boys and girls aged from eight to 15 on an annual basis.
A sister Academy will open in Los Angeles later this year.
Beckham, who is not looking to make any financial profit from the operation, is working in partnership with the Anschutz Entertainment Group to build his Academy.
Anschutz are developing a 26,000 capacity venue for sports and entertainment on the Millennium Dome site.
Asked if he could be more involved in his academy if he joined a London club after leaving Madrid, Beckham laughed: "I knew that one was coming, but no that's not in my plans either."
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