Parker has been left out of Spurs' starting XI for the past three matches and is expected to play no part in Sunday's final game of the season against Fulham. Redknapp says Parker will also miss England's pre-tournament training camp, which begins on May 21 in Spain, casting doubt over the whether the midfielder will be fit in time for the Three Lions' opener against France on June 11.
"He's had a problem with his Achilles, I hope it's not going to get worse," said Redknapp. "It isn't getting any better. It's a long-term concern.
"The way he is at the moment, he is struggling for fitness. It's not a rupture but it is sore. It is bothering him. After Sunday he will have some injection in it and we'll see if that can clear it up.
"He's been carrying it a few weeks. Maybe the only cure is a bit of rest but maybe the injections might clear it up. The specialist thinks it will clear up but it will need 10 days rest afterwards."
Meanwhile, Redknapp, who was overlooked for the England job with the FA instead appointing Roy Hodgson, is considering withdrawing his offer to be a BBC pundit at Euro 2012. Eight days ago the BBC announced that Redknapp would be part of their team in Poland and Ukraine for the European Championship.
"I'm still trying to make up my mind [about the position]," said Redknapp. "I will look at it in the summer. It could be tricky. I wouldn't be criticising [Hodgson] in any way so I suppose there's not much point having me on!
"I just feel like I need a holiday. I need to get a break from it all. Maybe I'll go to Canvey Island or the Isle of Dogs or something."