Let me clear up the issue once and for all. There are three commonly used constructions for expression of such things:
"I hope you don't mind my saying so."
In this case, "saying" (which is a gerund from the verb say and therefore functions as a noun) is the object of mind. "So" is an adverb modifying "saying." "My," in this case, is a subjective genitive form of the first person pronoun--note particularly that it is subjective (not in the usual way that people use the word subjective, but rather in the fact that "my" serves the role of the subject in the implied clause: "I say").
"I hope you don't mind me saying so."
In this case, "saying" (which is a present-tense active participle) is an adjective modifying "me," which is the object of "mind." Therefore "me saying" is the object phrase of "mind." Again, "so" is an adverb modifying "saying."
"I hope you don't mind (that) I'm saying so."
In this case, "(that) I'm saying so" is an object phrase--this entire thing is the object of "mind." Note that this is an example of an indirect statement, which is a common construction that takes the form of "[special verb] that* [dependent clause]" or "[special verb] ([direct object of the verb, which serves as the subject of the indirect statement]) [infinitive with implied subject that is the same as that of the previous verb or the one specified as the main verb's direct object]." Therefore, in the above bolded sentence, "I" is the subject, "am saying" is the verb, and "so" is an adverb modifying "am saying," all of which combine to create a clause dependent upon the word "mind."
* In colloquial speech/writing, the "that" is often omitted.
I hope that this explanation clarifies the matter.![]()





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