According to mlbtraderumors.com, Rhodes is on pace to be a Type A free agent.
The net of this is that if the Reds offer him arbitration and he declines it and pursues FA, the Reds get a 1st rounder (if the team is in the bottom half of the 1st rd) or a 1st rd comp pick (if the team is in the upper half of the 1st rd).
It's quite possible that, if the Reds offer him arb, that he will take it. The past few years have shown teams to be quite reticent to sign type A players that aren't truly impact players.
Given his age and type A status, I don't think it's likely the Reds will extend him. Rather, they'll offer him arb and simply agree on 1 year deal with him if he takes it.