Why not just sign it and put all the speculation to rest? If he is staying this cant be helping with recruiting or current players.
Normally, when coach extensions are announced it is after they are already signed, not when they are offered. I understand OM putting the word out about the offer so the AD can say "hey, we tried to lock him in" in the event Lane is leaving.

As I see it the only benefit to delay signing the extension, if he is staying, would be to garner some extra media attention at the presser when he makes the announcement to stay.