It has been reported in the Evening Standard that Tesco and Lidl have begun a High Court fight over the use of a yellow circle logo.
German discount chain Lidl says a trademark, and copyright, has been infringed, while Tesco has made a counterclaim.
Lidl uses a yellow circle in its main logo, and Tesco uses one to highlight offers available to members of its Clubcard scheme.
A judge began overseeing a trial at the High Court in London on Tuesday.
The hearing is due to end next week.