The on-loan striker has shone for Tottenham since completing a switch from Manchester City, but he is struggling with a hamstring problem.
His presence would be missed should he be forced to sit out a trip to Newcastle this weekend, with Spurs looking to build on the momentum they established before the international break.
Redknapp is, however, reluctant to push Adebayor too hard and risk losing him for a prolonged period of time.
He told Sky Sports News HD: "He has got a bit of a hamstring. He played on with it last week. He did it in the first half against Arsenal and he played on, which is not easy. He did have a tear. It's touch and go for him really.
"It's a dangerous one. If he tears it badly, he has got a grade one tear if he makes a real mess of it and he could be out for six or seven weeks.
"It's a difficult one to risk him, but we will see how he feels. We will give him a couple of days yet, keep treating him and hopefully he could be okay.
"If he is a doubt, I wouldn't want to risk him. I wouldn't want to lose him long term."
Adebayor is not the only doubt heading into Sunday's meeting with the Magpies, with the latest round of international fixtures having done Tottenham few favours.
"We have got one or two little knocks," said Redknapp.
"I lost a couple of boys last night [Tuesday] playing for Croatia - [Vedran] Corluka and Niko Kranjcar both had to come off with injuries. They are getting scans today [Wednesday].
"Sandro, as well, picked up a calf last week, so we are waiting to see how he is. We have got one or two niggles but hopefully we'll be okay."
Rafael van der Vaart's fitness is also a concern, with the Holland international having struggled to shake off a niggling hamstring complaint.
"He sometimes has a problem with that Rafa," said Redknapp.
"He has had a few hamstrings since he's been with us, but he's important to us - he scores goals. He's an amazing finisher. Last season I think he got 12, this season he's capable of getting near 20 goals from playing in that position where he likes to play. "