The newspaper said that Institutional Shareholder Services (ISS), a stock investor advisory firm, issued a report saying Apotheker and the three directors violated HP's own rules regarding the nomination and independence of board members by their participation in nominating five new people to the company's board of directors.
Their participation in the nominations compromised the independence of those board members.
The ISS recommended that shareholders of HP vote against the three directors of HP involved in the nominating controversy and to reject Apotheker's proposed pay package, which it valued at $47 million, due to his role in nominating the new directors.
The HP board has seen its share of controversy over the past year, from the resignation of former CEO Mark Hurd amid sexual harassment allegations to the appointment of Apotheker, former CEO of software vendor SAP, which was being sued by Oracle over alleged theft of intellectual property. Apotheker never appeared at the trial, in which a jury awarded Oracle US$1.3 billion.
The board has faced criticism over its handling of Hurd and its choice of Apotheker.
Neither ISS nor HP could immediately be reached for comment.