The Spurs full-back says he and his team-mates will look to put the young Spaniard under as much pressure as possible after two errors in as many games since joining United
The 20-year-old has made a shaky start to his career at Old Trafford, making mistakes in each of his first two competitive matches for the Red Devils.
Assou-Ekotto told reporters: "We will try to take advantage of these problems he's had.
"When you come to England you have to learn quickly how we play here. It is never easy in the first six months."
Assou-Ekotto is likely to come up against another of United's summer recruits in Ashley Young at Old Trafford on Monday, but the Cameroon international says he is not fazed by the prospect of facing the England international.
He continued: "We used to play against him when he was at Aston Villa and we did OK against him then.
"So it will be the same against Manchester United - he's not better just because he has changed clubs.
"Young and Nani are both good players, but they are still only human. I really don't care who I play against from Manchester United."
United will be missing several key players for their clash with Spurs, including first choice centre-back pairing Rio Ferdinand and Nemanja Vidic.
Assou-Ekotto continued: "United have some injuries at the moment and I hope this will help us. But the problem with them is that even when they miss some players and don't play well, they are still good.
"They never lose. The minimum they do is 0-0 or 1-1, but they don't lose. So it will not be easy for us."
The defender also backed Tottenham's move for Manchester City striker Emmanuel Adebayor, who is set to join the club on a season-long loan deal.
"I played against him when I was young [in France] so I know him well," Assou-Ekotto said in the Daily Telegraph.
"He is a little bit like Peter Crouch but with more mobility. He will find a good complicity with Defoe because Jermain is used to playing with that style of player.
"We saw what he did against us in Madrid last season, so I am sure he will help us.
"If the manager signs him it's not to finish fifth or sixth. He's a player from one of the big four and if we get a player from one of those clubs, it's for Tottenham to finish in the big four.