Ivory Coast defender Aurier posted a video of himself training with Tottenham team-mate Sissoko on Instagram on Tuesday.
The 27-year-old, who was wearing a mask, has since deleted the videos, which showed him running shuttles and sitting next to France midfielder Sissoko, disregarding the current social distancing advice.
Aurier and Sissoko are the latest high-profile figures at Tottenham to ignore the guidelines while Britain is on lockdown due to the pandemic.
Just two weeks ago, Tottenham manager Jose Mourinho was pictured holding a one-on-one training session in north London with French midfielder Tanguy Ndombele.
Mourinho was forced to admit his mistake, saying his “actions were not in line with government protocol”.
On the same day, Tottenham duo Ryan Sessegnon and Davison Sanchez were filmed running side-by-side, while Aurier has also posted a separate video of him running with a friend.
Government guidelines say you can only exercise outdoors on your own or with members of the same household.
“We shall be speaking to both players involved,” a Tottenham spokesman said.
Download our app and read this and other great stories on the move. Available for Android and iOS.