The Welsh left-back has played second fiddle to his English counterpart thus far, with Rose starting all three of Tottenham's Premier League outings.
However, Coleman says that the 21-year-old, who joined Spurs from Swansea City in the summer, must be ready to capitalise when his teammate slips up.
"I think Ben will end up being their first choice," he told reporters. "He is a top player and a great lad, he will settle in there.
"It is not always easy when you have a big move. Ben is a Swansea boy and we don't tend to be great travellers when we are young.
"Danny Rose has not done anything wrong, but all players have a bad day, and when he does and Ben gets his chance we know he is good enough. It may take him time but I have no doubts he will make it work and play a lot of games for Tottenham."
The Lilywhites sit sixth in the Premier League table after picking up two wins from their opening three games.