Pietersen has been suffering with the strain since the second test at Lord's but batted in the indoor nets for almost an hour on Wednesday and then underwent a short fitness test on the outfield, with strapping filled with a liquid visible on his leg.
"Pretty good," Cook told a news conference when asked about the chances of England's most explosive batsman playing.
"He has gone through training the last two days and done everything we asked of him. Fingers crossed."
James Taylor, who has two caps and scored an unbeaten century against Australia playing as a ringer for Sussex in last week's tour match, has been included in the squad in case Pietersen is ruled out.
England lead the five-match series 2-0 and will retain the Ashes with a win or a draw in Manchester.
Australia captain Michael Clarke, who has a slight worry over Steve Smith after he failed to train because of a minor back problem on Tuesday, was due to speak to the media later with his side's lineup very much uncertain.
(Editing by Clare Fallon)
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