Should it be
Last years data set contains information that the reports can work off
Last years data set contains information that the reports can work of
Should it be
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(The earlier question “Based on” instead of “based off of” covers some similar ground).
Some people (myself among them) dislike "Data the reports can work off of", but that's not one of OP's proposed alternatives, so let it pass.
Of OP's two, "of" would never be acceptable. For many people, "off" would be okay, but I think most would prefer "with", "on", or "from". My preference is for...
There's not necessarily any semantic/grammatical argument for any particular preposition here, and all those I've emboldened (apart from of) are actually used by competent speakers. But I personally feel it makes more sense for actual programs to work on or with data because they do "more" with that data. To some extent, reports can be said to just list data from a database.
(I changed OP's "information" to "data" because I think one of the purposes of reports is to turn data into [accessible] information.)