If you can fork your opponent's king and knight with your knight, then your opponent must either take your knight or allow you to take theirs on the next turn. Since that gets you down the KN vs K one way or the other, this forces the draw.
However, the answer to the literal question is no: there is no situation in KN vs KN where the only legal move is to take a knight. Here is a case analysis, assuming White to move.
White is checkmated. Then, by definition, White can't take anything.
White is in check, but not mated. The check must be from the knight, so White can't take it with their king. If white's king is not in the corner, they can simply move their king out of check (there are at least five adjacent squares; the black king might block three of those, and the white knight one more, but that still leaves an escape square). If the king is in the corner, the black king covers at most two of the three adjacent squares, and the third one can't be occupied by the white knight because that would be checkmate; so there's still an escape square.
White is not in check.
- If the white knight is not in a corner, it can move to at least three squares. The white king could be on one of these squares, the black knight could be on another, but the black king can't be on any of them (it's White's move, so Black can't be in check). Therefore, white has at least one possible knight move that isn't taking the black knight.
- If the white knight is in a corner, there are two squares it can potentially move to. If either of these is empty, White has a non-capturing knight move. If they're both occupied, we're in a position such as the one below. Wherever the black king is, White has at least one king move that doesn't capture the knight. But note that this position is another one where the white knight can be captured on the following move.
[FEN "8/8/8/8/8/6n1/5K2/7N b - - 0 1"]
So perhaps the more interesting question is whether we can force the transition to KN vs K, rather than specifically forcing the opponent to take our knight. Again, the answer is no: as long as you keep your knight out of the corners and avoid having your king and knight forked, you can force the game to continue for 50 moves. The only way this could go wrong is if your knight starts in the corner and the opponent can force it off the board before you can get it out, as in the following position
[FEN "K7/8/2k6/8/4n3/8/8/7N b - - 0 1"]