Didn't happen like that at all.
Kurt certainly clowned Lesnar in a very famous story but it was at a WWE event back in 2003. Dana White was not there, nor has Dana EVER offered Kurt a UFC contract apart from a heavily rumoured spot on the Tenth TUF where Kurt allegedly failed the medical.
He was certainly an amazing wrestler & if the UFC would have been paying much bigger money after he won his Gold medal then he could have had a great career. But instead he went with the much bigger bucks in the WWE, although since then Kurt has repeatedly floated the idea of an MMA career but all that ever was about was getting himself some attention. Age & multiple serious injuries from both his amateur & pro wrestling careers meant that was always a non-starter.
The closest he's ever come to an MMA fight was playing Koba (based on Fedor) in the Tom Hardy film "Warrior", beating up Eddie Guerrero backstage after a Smackdown match went wrong & Daniel Pudner nearly snapping Kurt's arm like a twig.