Espirito Santo, 52, is expected to leave West Ham this summer following their relegation from the Premier League.
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The Portuguese boss took over from Graham Potter back in September but was unable to steady the ship and secure survival.
According to The Guardian, the club are keen on talking to Parker, 45, and O'Neil, 43, over potentially taking over.
Parker, who played for West Ham has been out of work since leaving Burnley after their relegation was confirmed.
O’Neil on the other hand is under immense pressure at Ligue 1 side Strasbourg following their disappointing end to the season.