Canadian permanent residence alone does not qualify a person for TN. The nationality requirement is citizenship of Canada or Mexico. If you are a Mexican citizen living in Canada, that citizenship may provide the relevant nationality basis, subject to the Mexican procedure and all other TN requirements.
Answer the nationality question before preparing a Canadian case
Review your current passport and citizenship records rather than your Canadian address or PR card. A pending Canadian citizenship application, long residence or a U.S. employer’s willingness to support you does not create Canadian citizenship for TN purposes.
If neither qualifying citizenship is held, assess the offer without treating TN as presently available. Any alternative immigration route requires its own analysis; this overview does not determine whether a different category would fit. Approach the timing question separately from the eligibility one.
A person who expects to obtain Canadian citizenship at some point may well have a route later, but planning cannot proceed on a document that does not exist, and no part of the process can be started on the strength of an expectation. In the meantime, establish what the current nationality does permit, since the answer is frequently more useful than people assume. A Mexican citizen holding Canadian permanent residence is a Canadian resident and a Mexican national, and TN is available to qualifying Mexican citizens through a procedure that differs from the one Canadian citizens use.
Where the nationality held is neither Canadian nor Mexican, TN is not available on any basis and the conversation should move to whether some other classification fits the role and the person.