Even though William Shatner has been offered a role in The Big Bang Theory, he has not yet appeared on the show.
The reason he declined a part was dissatisfaction with the role offered.
“I’ve had several conversations with the creators, and what they wanted me to do, didn’t seem to be exactly right, so I said ‘find something that’s better’. They may have taken umbrage at that, I’m not sure.
“They wanted me to play myself a little obliquely, and they said it would work out, but I needed more assurance on that.”
Source: Digital Spy