The boss was speaking to World Football Daily who appear to broadcast a phone-in in the USA and Jones was a guest on Wednesday evening. Cardiff City have not made an official announcement of the Naylor signing but Jones makes it clear he is a Bluebird.
"We've just signed Lee Naylor this evening from Celtic," Jones told the presenters.
When quizzed as to whether this was a part of the deal that saw Joe Ledley move to Celtic, Jones said: "No, Lee was out of contract and he's now just gone through all his medicals and everything's been agreed and he's signed, so he'll be joining the party tomorrow now.
"We're trying to build because we let ten players go at the end of the season.
"We lost Joe Ledley to Celtic, that was a big loss to us, and slowly but surely we're getting out numbers back up with players of good quality who should stand us in good stead."
Jones also explains how he started to speak to Craig Bellamy about the idea of him coming to Cardiff City.
You can view the footage here on You Tube.