The approach comes as WPP is in the midst of a root and branch review of its business as part of a post-Sir Martin Sorrell overhaul, which includes the sale of a majority stake in research division Kantar.
WPP acquired Finsbury 18 years ago but Rudd is keen to regain control of the business, reportedly opening discussions with both Finsbury and WPP about how such a deal might take place – although neither party has commented publicly on the matter.
Options on the table are said to include a full buy-out at over £100m or some form of equity acquisition.
WPP is in process of significant reorganisation under a new leadership team led by chief exec Mark Read, divesting itself of some businesses and merging other agencies as it seeks to halt a sharp reversal in its share price.
The holding group has been significantly reining in its activities to focus on its core advertising and marketing offer.