The 35-year-old midfielder is hoping to clinch a temporary move to the Premier League during the MLS off-season with fourth-placed Tottenham Hotspur keen to do business.
However, Keegan said the former Manchester United and Real Madrid player would find it difficult.
"I think it's too high risk. If I were a manager I don't think I would do the deal because there's a chance it could upset the apple cart," Keegan told Reuters at the launch of broadcaster ESPN's FA Cup Third Round coverage.
"You would get a lot of publicity. It might work but it might backfire. It's a risk. But Harry (Redknapp) may think it's a gamble worth taking.
"There are lots of reasons to do it but just as many reasons not too. I'm sure he still has something to offer because he's a clever player and he is still doing the same things now as he did when he was 20.
CHOOSE CAREFULLY
"If I were him I would choose very carefully what club to go to. Plus, if it's only six or seven weeks I don't think that's long enough. It would take two or three games to pick up the pace of the Premier League and then there's a chance of picking up an injury.
"If I was the LA owners I would be saying to him go and get a rest and come back with your batteries charged but he just wants to play football and you can't criticise him for that."
Steve McManaman, who played alongside Beckham for England, also warned Beckham would not have the chance to show his best.
"He has huge experience, his possession of the ball is still very good and his delivery is still good," said McManaman who won the Champions League with Real Madrid.
"But he would have to hit the ground running and that's the problem for the likes of Tottenham that it would only be a six or eight week thing.
"He would want to show his best form but it would be hard in such a short space of time."
British media have reported that LA Galaxy are happy to allow Beckham to go on loan providing various clauses are met.
Last season the former England captain suffered a serious Achilles tendon injury while on a short-term loan with AC Milan, ruling him out of the World Cup finals.
