The Newcastle United icons disagree over the summer signing.
Shearer has recently criticised the 22-year-old Frenchman in his columns and on Match of the Day but Ginola is said to have taken offence to the former striker's comments.
Both are Newcastle icons and the subject of their debate is a man signed by Newcastle last transfer window for a fee reported by the Daily Mail among others to be £12 million.
Following suggestions of Ginola's discontent, Shearer offered the following riposte on Twitter:
Well done Ginola for putting Shearer in his place on Canal+ just now. Ginola (rightly) took offence to Shearer’s MOTD analysis of Thauvin— Matt Spiro (@mattspiro) September 26, 2015
Shearer, of course, isn't the only man to criticise Thauvin after a poor start to life at St James' Park. Sky Sports pundit Phil Thompson slammed the 'awful' summer signing after Newcastle's 2-1 defeat at home to Watford.
Interestingly, Thauvin was an unused substitute against Chelsea and Newcastle's performance and energy levels (up until a late collapse) were far superior without the 22-year-old Frenchman.
Whether the creative forward can come good at St James' Park remains to be seen but the case of Remy Cabella shows the Magpies aren't willing to wait forever.