Convolution theorem with a kernel smaller than the image

Suppose that I need to apply a convolution filter to an image. I want to do it by using the convolution theorem so I compute the kernel for the size of the input image to later calculate fft's and multiply. But I want the fft calculation to be less time consuming. The kernel loses its magnitude the further from its center, as usual. If I want to crop it, say, have a smaller kernel with only significant values, can I for instance compute its fft and later somehow extend the resulting frequency domain image of the kernel to fit the size of the input image, to later multiply them point-wise?