BBC Radio Solent reports Eisner has already informed manager Paul Cook of his interest in creating the role.
The former Walt Disney chief executive has made an offer to buy 100% of the League Two champions.
Cook is believed to want a firm input over any potential candidate to ensure minimal disruption to his set-up.
Portsmouth won the League Two title on goal difference from Plymouth Argyle on the final day of the season.
Cook won the title for a second time in his managerial career after leading Chesterfield to promotion in 2014.
Eisner's offer of £5.67m for Portsmouth plus an additional investment of £10m in equity will be voted on by club shareholders and members of the Pompey Supporters' Trust (PST), who currently own 48%.
Portsmouth are considering appointing a director of football next season, should Michael Eisner's proposed takeover of the club go through.