However the bookmaker has come up with some more unorthodox suggestions, including Apprentice judge Lord Sugar.
The Hackney-born businessman, who took his seat in the House of Lords in the same year as Lord Sacks, has been given odds of 250 to 1.
Paddy Power also put three wild-card candidates at odds of 500 to 1, including comedian Sacha Baron Cohen, Cambridge-educated like Lord Sacks and television personality and broadcaster Vanessa Feltz, the only woman on the list.
And although David Miliband is likely to be busy teaching politics to north London A Level students, or with a non-executive role at Sunderland Football Club, Paddy Power has named the former foreign minister as a possibility.
Lord Sacks will have served 22 years as chief rabbi when he retires.
