Milan's poor results last season denied them a place in the lucrative competition as they had to play in the UEFA Cup.
But they have virtually ensured a place in next season's Champions League as they lie third in the Serie A table on 54 points, eight ahead of fifth-placed Fiorentina with 10 matches to go.
"I dream of playing the Champions League with Milan next season. I miss it very much and would love to score the winning goal in the Final," Beckham told Gazzetta dello Sport on Saturday.
"If it was against Manchester United? Well, that would be a problem, but if that happened next season I’d still want to win it, even if I support United."
The England midfielder joined Milan from Los Angeles Galaxy on a loan deal that was due to expire on March ninth.
He reached an agreement with the Galaxy officials to stay at the Rossonerri until the season's end before returning to the American outfit in a 'timeshare' deal from July to November.
Beckham, who said he was enjoying playing with Milan, is then widely expected to make a permanent move to the seven-time European champions in January 2010.
"Milan are special for everyone who loves football," the 33-year-old said.
"You hear their history, but don’t realize what it really means until you are involved. I’m not just talking about the players.
"Everything here is special, from the infrastructure to the people who work here, from the chef to the cleaners. It is a unique place, I’ve never seen such dedication to football."