Russian billionaire Zingarevich took over Reading in May 2012, purchasing a 51 percent stake in the club from Madejski.
Zingarevich pledged to be a long-term investor but has not been seen at a game since last September, leaving Madejski with the task for finding a new owner for the Championship outfit.
Madejski revealed that no firm offers have been made to buy Reading, however, he has insisted that the money is there to help the club progress after they missed out on a play-off berth on the final day of last season.
"As chairman, I would like to confirm that we have the necessary funding in place to safely take the club forward," Madejski said in a statement.
"Together, we continue to look for new ownership of the club and, as the wealth of speculation can attest, there has been plenty of interest but no firm offers.
"However, it is imperative that there is no rush to judgement and that we take the necessary time in choosing the right person for the future of Reading football club.
"While there is no takeover with any new investors, the process is ongoing. I would like to take this opportunity to assure our fans that the club is secure going forward.
"The club can announce that directors Anton Zingarevich, Christopher Samuelson and Andrew Obolensky have left the board."
