The Algerian midfielder starred for his nation as they secured a spot in the last 16, but was unable to help them overcome Germany.
Everton are also said to be looking at the 24-year-old, but Spurs may beat them to the punch as they plot their own transfer moves.
Brahimi is thought to be ready to leave Spanish club Granada on the back of his showings in Brazil, with the Premier League a tempting proposition.
Tottenham have his international team-mate Nabil Bentaleb in their ranks, which may give them an advantage over other suitors.
An attacking midfielder primarily, Brahimi is also able to play from a wide role and has long been tipped as a player to watch.
He netted once at the World Cup to help his nation advance from the group stage for the first time in their history.