From the Knox Co. Election Commission...

Absentee Ballots must be returned to Election Commission by USPS, FedEx, or UPS by Close of Polls on Tuesday, November 3

Knox County Election Commission reminds voters that absentee ballots cannot be hand-delivered to polling place or KCEC office

Knoxville – Knox County voters that have received their absentee ballot in the mail and haven’t yet mailed it back (or that will receive it in the next few days) can - with a first-class stamp for postage - drop it off at:

Downtown Knoxville Post Office
501 W. Main Street
Knoxville, TN 37902

by 3 pm on Tuesday, November 3 to help ensure that those ballots will be delivered to the Election Commission by the close of polls on Election Day.

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According to the TNDP, USPS has designated one post office in each of Tennessee's 95 counties for this accommodation.

UPDATE: From the Secretary of State...

The deadline to request a by-mail ballot has passed. To facilitate timely receipt of voted absentee by-mail ballots on Election Day, the U. S. Postal Service has designated a post office in each of the 95 counties for voters to expedite the mailing of their completed absentee by-mail ballot. Voters are requested to mail their ballot by 3:00 p.m. local time November 3 at the post office designated for the county. County election officials will pick up the ballots after 3 pm on Election Day. Tennessee law does not allow for third party political operatives to collect ballots on behalf of voters. Click here for a list of designated post offices.