Beckham has been training with Spurs for the past week as the club attempt to strike a deal to bring him to White Hart Lane on loan.
Redknapp wants the 35-year-old to stay until at least the middle of March, but Galaxy are refusing to budge on their demand to have him back in California for pre-season training in February.
With the clubs struggling to find common ground, Redknapp is ready to pull up stumps. "If it was only until February 10 that would only be a month," Redknapp said. "To do that would be a waste of time because, by the time David got fit, it would be a couple of weeks and suddenly you'd be into February.
"I would have liked him to play, if he could have come to the end of the season it would have been great. I didn't know it was only going to be two months at best.
"When it was mentioned, I thought 'yeah, to the end of the season it would be good'. Then, suddenly two months becomes a month, and only if we got permission.
"By the time he's fit, just to throw him in for three or four games would be difficult."