Maybe you do not really mean "direct conversion" receiver. A direct conversion reciever has a baseband output. You can lowpass filter it to remove higher frequency components, and that lowpass can have a tunable corner frequency. Such a lowpass filter can be an analog filter, or a DSP digital filter, or a combinaiton of both. Also, you can highpass filter the baseband (with a series capacitor) to remove DC. But that is about it for filtering.
For communicaitons filters, typically you downconvert the rf signal to a "low IF frequency", instead of downconverting it to 0Hz center, and that allows you to bandpass filter the signal's width. For communicatioins systems, you set that bandpass filter to be just a little bigger needed to send the data rate through it, and that helps to reject "out of band" signals that might jam your reception.