Jesus could have said the latter, but the ones whom he addressed were Israelites and as such were already witnesses of Jehovah.
لِأَنَّ تَلَامِيذَهُ ٱلَّذِينَ وَجَّهَ إِلَيْهِمْ كَلَامَهُ كَانُوا إِسْرَائِيلِيِّينَ ،‏ وَبِٱلتَّالِي كَانُوا أَصْلًا شُهُودًا لِيَهْوَهَ .‏