Use the ing-form. CB
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AnonymousWould he has suggested work.Wrong. Would + has is impossible.
AnonymousWould it be correct to say:He has suggested I ask you for ...Yes. Both "He has suggested" and "He suggested" are correct. If you mention a specific time when this happened, use only "He suggested". (Last week he suggested that I ask ..., but NOT Last week he has suggested that ....)
Anonymousif I don't mention a specific time when this happenedIn that case you can use either one and your sentence will be grammatically correct.