The Spurs boss is hopeful over the midfielder’s fitness, but conceded that his participation in Ukraine and Poland this summer could be in jeopardy if the problem persists
Parker, who missed Spurs’ win over Fulham last weekend, has had an injection in a bid to resolve the problem.
With Roy Hodgson set to name his provisional squad for the tournament on Wednesday, Redknapp remains hopeful that the midfielder will be fit enough for the finals, but conceded that he is likely to miss out if the problem persists.
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"He has had an injection and hopefully that will do the trick," the 65-year-old told Sky Sports News. "It should settle it down, it might be seven or eight days and then he could be okay to start training again and playing.
"I just hope he is going to be okay for the Euros for his sake and for England as well.
"If the injection doesn't work then obviously he has got a problem, we will have to see where we go from there and see if something more drastic is done.
"I think they [the medical team] are quite confident the injection could do the trick, so let's hope so."
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Redknapp has backed four of his Spurs side to earn a place on the plane to Poland and Ukraine, stating that Aaron Lennon, Jermain Defoe and Kyle Walker are all in with a chance of joining Parker in the squad.
"Yeah I am sure they have got a chance - Aaron, Jermain, Kyle Walker and Scott - so I wouldn't be surprised if four of them made it but I wouldn't be sure," he added.