The 36-year-old former England captain said his serious suitors included "one or two" English Premiership clubs, although he declined to name them, as well as Paris St Germain - the French club touted in December as the front-runner to land him.
"It was fun watching it, to be honest," Beckham said on Thursday at Staples Centre arena, where the media assembled for his welcome-back press conference showed his continued drawing power.
"Everyone else was talking about it. I always said at the end of last season that there was a good possibility that I was coming back."
The player who won six English Premier League titles with Manchester United was pressed on just which English clubs made offers.
"One or two," he repeated. "It was one or two."
Beckham helped Galaxy capture the MLS Cup league title in November, shortly before his ground-breaking five-year MLS contract expired.
In December, it was reported in France that Paris St Germain had signed him - and that his wife, Victoria, had been scouting schools in the French capital for their four children.
Not true, Beckham said, noting that his wife, a pop star turned fashion designer, often visited Paris for her own work.
Beckham said he and his wife made the final decision to return to Los Angeles over a glass of wine at their London home on New Year's Eve.
He said he needed a few weeks after the emotion of lifting the MLS Cup to consider his options.
"I just needed a break," Beckham said.
"I needed to get away, to rest my body and then to decide what I felt was the right move."
Beckham, who signed a two-year deal to remain with Galaxy, said he considered leaving the MLS on a high note, and even retirement, although he later said that wasn't really a serious option.
"To be honest, retirement was never a part of my plans," the 36-year-old said.
"It had been talked about by other people, but it always is when you get to this stage of your career."
Beckham has nothing to prove in the MLS, but that doesn't mean the English football icon can't see plenty of work to do now that he has opted to return to Los Angeles.
"It's not unfinished business - it's just doing it over again," said Beckham.
"I've never come back after a season with the Galaxy and been a champion.
"I wanted to have that feeling. We're not finished. I'm not just happy with one championship, I want more."
Beckham, who will turn 37 in May, accepted a two-year deal from Galaxy that has been reported to be worth $15 million.