Be warned, it appears that a player you pick up off of waivers that's in the last year of their contract can not be extended. I've got a few in 75 that I was hoping to extend after picking them up, but the contract button isn't present.
That sounds like a glitch that JDB could fix. It's possible that the players previous team only signed him to a one year contract which would make him ineligible for an extension.
When you sign a player off waivers, you are taking over the contract - so all restrictions still apply. You should have seen a warning when you made the offer.