Bush said it was up to Johanns whether he would seek another political office, but added that he thought Johanns would "make an outstanding member of the United States senate."
Three other Republicans already are in the race for the nomination to succeed Republican Chuck Hagel, who is retiring as Nebraska's senator.
They are Jon Bruning, state attorney general, Hal Daub, former Omaha Mayor and Pat Flynn, a financial advisor.
Among the state's Democrats, Bob Kerrey, a former senator, is also said to be considering a run.