The personality is a committed Christian and has spoken about his faith in the past.
In a new interview for the Radio Times he said he would not work the Sabbath no matter how good the offer.
"If the BBC said, 'Dan, we want you to be the main presenter on Sports Personality of the Year but as you know it's on Sunday night,' how would you answer?," asked interviewer Eamonn Holmes.
Walker replied that he had these "large and significant carrots" before but his faith was stronger than the pull of a job.
"I'd say, 'I really appreciate that. It's a lovely offer and I'm sure it would be a magnificent programme but someone else can do it, because for me Sundays are even more important than the best job in the world'," Walker said.
"But as a Christian, I'd say that some things are more important than even the best job in the world."
He added: "For practical and spiritual reasons it's really important to me. It's a personal decision I made for the good of my family, and I've managed somehow to maintain it for 20 years. I'm in the job because I love doing it, but it's not the be all and end all."
In the same interview Walker revealed how he found out about the death of his friend Wales manager Gary Speed in 2011.
"I was in church the next day and my phone was going absolutely bonkers. Every 10 seconds I was getting text messages, phone calls, so I said to my wife, 'Something's happened. I've got to go'," he said.
