Both are correct, but it's actually more popular to pronounce the first "i" in "depreciation" (the vowel in the third syllable) with the vowel of "bee."
Variation like this between /iː/ and /ɪ/ occurs in specific, predictable contexts: at the end of a word (usually written -y) or in an unstressed syllable before another vowel (usually written -i-). In these contexts, there is no contrast between these sounds, so they are often grouped together under the name of the "happy vowel." Traditionally in some British accents (including the prestigious "Received Pronunciation") words like "happy" were pronounced with the /ɪ/ vowel of "kit" or "bit." But Americans, and many British speakers nowadays, pronounce words like "happy" with the /iː/ vowel of "fleece" or "bee."
Geoff Lindsey wrote a blog article about it, "The fallac[ɪj]of schwee," where he recommends using the vowel of "fleece" or "bee" (ē or /iː/) for this sound even if you're trying to use a British accent.