Use "would". However, I think you mean "forgot", not "forget". Am I right?
I forgot that you would be working today.
Exact words: "I'll be working today."
Do you want to go to the park?
I can't. Don't you remember that I said I would be working today?
Oh, yes, I forgot that you would be working today.
You could also say, "I forgot that you were working today."
I think this is okay, though grammar books caution, I think, that this is "informal". "I forgot that you'll be working today." I like using "would" better in this sentence. So, yes, use "would". I knew that I would say that.
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