The Kuzari [1/115] writes:
So we see that he holds that geirim cannot be prophets. Rav Gifter ztz"l [Hadarom 42 page 174] explains that a ger is excluded from קהל השם and thus may not receive prophecy. This would also exclude a mamzer.
The Rambam never excludes a ger from nevuah. However there is a Rashi in Sanhedrin [39b] that would bolster the opinion of the Kuzari. The gemara asks in what merit did Ovadiah Ha-Ger merit prophecy? Rashi explains that geirim are generally not allowed to be prophets.
The Meshech Chochma [Devarim 18-15] says that geirim can only prophecy about goyim but not about the Jews [see there].
There are numerous questions on this Meshech Chochoma. PLEASE see the שעורי משמר הלוי on Sanhedrin [15] and you will be enlightened. See also מעליות קובץ כ' מעמ' 174.
ויש להאריך ומה שהלב חושק הזמן עושק!!
