How to pass async function to Pool.map()?

Question

The following code will get the error of

multiprocessing.pool.MaybeEncodingError: Error sending result: '[<coroutine object f at 0x000001EA90528CC0>]'. Reason: 'TypeError("cannot pickle 'coroutine' object")'

from multiprocessing import Pool

async def f(x):  # removing async works
    return x * x

if __name__ == '__main__':
    with Pool(3) as p:
        print(p.map(f, [1,2,3]))

How to use Pool.map with asynchronous function?