Former AB InBev CMO Miguel Patricio joined the food marketer as chief exec last summer.
Process takes place as Unilever considers selling off tea business.
Food giant will also increase working media spend by 30%, with even bigger boost for key brands.
The review includes work around sustainability, according to people with knowledge of the matter.
Brands include Davidoff, JPS and Parker & Simpson.
Mindshare is expected to give up Fox account in Europe.
Top news, insights and analysis every weekday
Sign up for Campaign Bulletins