Andrew Fisher is close to being named as Scott Forbes' successor by the FTSE-100 company.
City sources said that Fisher's appointment could be announced within weeks.
Rightmove has been hunting for a new Chairman for several months.
Forbes' departure had become inevitable under revised corporate governance guidelines which deem that listed company chairs are no longer independent after more than nine years on the board.
He has been a director of the property portal since 2005.
Rightmove has seen its shares perform strongly, despite the UK's sluggish housing market.
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