The West Brom striker - who arrived shortly after 9am - is fighting a Football Association misconduct charge over his use of the gesture while celebrating a goal at West Ham in December.
The 'quenelle' has been linked to anti-Semitism by some politicians in France, although Anelka maintains the gesture - popularised by his comedian friend Dieudonne - is merely "anti-establishment".
An independent regulatory commission is hearing the case, and Anelka faces a minimum five-match ban if he is found guilty of breaching the FA's anti-discrimination rules.
The first day of the hearing was taken up with the FA's case - put forward by QC Paul Grainey - and Sky sources understand the second day will be given over to Anelka's team to put their case forward.
Anelka's QC is Pushpinder Saini - who reportedly earns around £100,000 a week and whose bill is understood to be being paid for by Anelka himself as West Brom have said he must pay his own legal fees.
The hearing is expected to run for the rest of the week, with a decision due on Friday - although West Brom have said they will subsequently also hold their own inquiry.