how to get area of rectangular that the player went through its edges ?

Firstly,I don't know if my question title is true but I couldn't find better title, sorry If I titled wrong.

I'm trying to grid base game. The player is moving grid to grid and never stop between grids even if ıt takes command to move another direction between grids.

So, I want to get area of grids where the character walks on the edge of area.

To clarify myself

Player starts to move and tries to reach edge following brown lines. When player reaches any edge, the all tiles should be colored.