To find the area of the largest circle that can be drawn in a square, follow these steps:

1. Determine the side length of the square:
The area of the square is given as \(196 \text{ cm}^2\).
\[
\text{Side length of the square} = \sqrt{196} = 14 \text{ cm}
\]

2. Determine the diameter of the circle:
The largest circle that can be drawn inside the square will have a diameter equal to the side length of the square.
\[
\text{Diameter of the circle} = 14 \text{ cm}
\]

3. Determine the radius of the circle:
\[
\text{Radius of the circle} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \text{ cm}
\]

4. Calculate the area of the circle:
Use the formula for the area of a circle, \(A = \pi r^2\).
\[
A = \pi \times (7)^2 = \pi \times 49
\]
\[
A \approx 3.14 \times 49 = 153.86 \text{ cm}^2
\]

Rounding to the closest option provided:

A. 154 cm²