Since Monday, she has been undergoing intensive debate tuition with Mr O'Donnell at John McCain's ranch in Sedona, Arizona.
Also present are senior McCain aides like campaign manager Steve Schmidt and foreign policy adviser Randy Scheuneman.
Mr O'Donnell will be "undoing" some of Mrs Palin's earlier debate preparation, according to the Wall Street Journal, which had resulted in her producing "rote" responses.
She "flubbed quasi-mock debates" last week, the newspaper alleges, leading to "finger-pointing" within the McCain campaign.
Her advisers will work with her this week "to make sure her responses use 'her words'", the newspaper quotes an aide as saying.
Whichever words she ends up using on Thursday, this year's debate will be one of the most fascinating nights of the campaign so far.