Yes, you may. "This morning" can refer to both past and future.

In my opinion, "this morning" usually is talking about a past action: "I cleaned my room this morning." "This morning I went for a walk." Saying something in the future, like "I'll go to the store this morning" isn't generally a correct statement, but saying "I'll go tonight" or "I'll go this afternoon" would be correct. You could also say "I'll go to the store tomorrow morning". But really, since morning time is early in the day, you wouldn't typically use a future tense because there's not a lot of action before it (since it's pretty early in the day). Same with present tense, in general you wouldn't really use it with "this morning." Most people would probably just omit it, because if it's going on at that time, it's understood that it's happening in the morning time, and isn't needed at all. (Sorry if that was confusing:/)