A small number of players and staff were sent home on Sunday after the tests came back positive. The academy was allowed to continue.
Talks between the club and the league have put the game against Brentford in doubt.
The first team operations at the Carrington Training Complex will be closed for 24 hours following confirmation of positive LFT COVID-19 cases among the first team staff and players.
People who tested positive are isolating. With the health of players and staff the priority, the club is in discussion with the league about whether the fixture against Brentford is safe to continue.
Team and staff travel to London will be deferred pending the outcome of that discussion.
The game between Spurs and Seagulls was postponed last week due to a severe coronaviruses outbreak among Antonio Conte's squad.
