We noted last week (originally reported by the Wrestling Observer newsletter) that TNA made a big play to get Alberto El Patron on their first show on Destination America. A deal was not reached because the sides were far apart on money. TNA was also trying to get Edge. Negotiations did not get serious and money was not discussed. It was described as TNA putting out feelers to see if he was interested.
The idea for Edge was to have made him the new authority figure on the show to replace Kurt Angle. Edge has a role on the SyFy series Haven so even if he wanted to accept an offer, it probably would have been a conflict for him.