Mr Klepec made the comments in a statement on Wednesday and was quoted in reports on Fairfax Media websites.
Mrs Rinehart holds about 18 per cent of Fairfax Media, and its existing directors are keen for her to sign the media company's charter of independence before any offer to join the board is made.
Mr Klepec said the board required new members to assist in making Fairfax more sustainable, as it has "plainly not delivered for the last several years of declining share value".
"We are certainly in support of journalist integrity and accuracy, these are important principles in journalism, and are keen to support an effective charter to endorse this in the interests of Fairfax Media, assuming one can be agreed," Mr Klepec said in the statement.
"Fairfax Media has an abysmal track record and our intention is should we be in a position to have sufficient seats to influence the board, which it is doubtful two seats would bring should only two seats be offered, we would like to aim towards making Fairfax Media sustainable."
Fairfax shares closed up half a cent at 55.5 cents.
- AAP