Appearing on CNN, Thompson was asked whether, as president, he would turn to Saudi Arabia for help as Bush did.
Thompson, a former Tennessee senator, said the problem was a "little bigger" than Saudi Arabia.
"It's not in the United States' long-term interest to go hat in hand begging people to do things that in the end we know they're not going to do," Thompson said.
"What we need to concentrate on is diversifying our own energy sources here in this country and opening up what oil reserves that we have here ... using nuclear more, using clean coal technology more and all the other things that we can do," Thompson said.