The midfielder has missed Spurs' last three games with an Achilles injury, something which Redknapp describes as "a long-term concern".
The former Chelsea and West Ham man has been a key figure in Tottenham's push for a Champions League place this term, earning himself a berth in the PFA Team of the Year.
Parker was also handed the England captaincy during Stuart Pearce's one-match stint as interim boss for a friendly against the Netherlands in February.
The 31-year-old is expected to miss out this weekend as Spurs face Fulham hoping to secure a top-four finish ahead of Newcastle, but Redknapp fears that Parker could miss England's pre-tournament training camp in Spain.
He told reporters: "He's had a problem with his Achilles, I hope it's not going to get worse. 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 tomorrow he will have some injections 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."
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