"Playing here is every footballer's dream," Beckham told Italian paper Corriere della Sera on Wednesday when asked if he would go back to the United States in March.
"But it's not easy to decide. It's a matter that requires time. I'm under contract with, and have lots of respect for, Galaxy," he added.
"But the possibility to play at Milan is something special. I knew I'd have fun but I didn't expect to have so much fun. Anyway, I am a very respectful person."
The 33-year-old midfielder, who scored his first Milan goal in the 4-1 win at Bologna last weekend, joined the club partly in a bid to stay in contention for England selection during the U.S. close season.
But the professional attitude and tactical acumen he has shown have led to calls for him to stay and Milan chief executive Adriano Galliani has said the seven-times European champions are willing to pay Galaxy a fee for him.
Beckham, who has started three matches for the Serie A club, said he was surprised at how quickly he has settled.
"Sometimes it takes weeks or even months to understand how a team plays or trains," he said, adding that he found Milan similar to his former club Manchester United.
"I must admit that everyone has done their bit to make me feel at ease. I've been welcomed really well."
He also said that playing in the U.S. had been frustrating at times.
"The U.S. championship is young. I think it will take 10 years more to hit big targets. I must admit that, having played in Europe, sometimes it has been frustrating to take part in certain games."
England manager Fabio Capello, who has flown to Italy to see Beckham play for Milan against Genoa on Wednesday, has hinted his good form would be rewarded with a call-up to his squad for the friendly in Spain on February 11.
"I'm happy for Milan and I'm happy for the national team," Capello said.
