The Tottenham Hotspur striker has started 61 matches for club and country since the beginning of last season and looked set to feature from the off on Tuesday night.
Sky Sports News claims that Southgate will instead give Kane a breather, though, with Danny Welbeck likely to be given the nod through the middle.
In the absence of regular captain Kane, it is suggested that clubmate Eric Dier will wear the captain's armband against the Swiss.
Jack Butland, James Tarkowski, Danny Rose, Kyle Walker, Trent Alexander-Arnold, Fabian Delph and Ruben Loftus-Cheek are also in line to start as Southgate makes mass changes from the 2-1 loss to Spain.
Tottenham head to Liverpool in a huge showdown when Premier League action resumes on Saturday.