Hobsbawm, head of agency HMC and a judge for this year's PRWeek awards, has been nominated by the college's school of marketing and management to take on the role.
She has already been an adviser on the setting up of the school's first Master's degree in PR, which starts in January.
If accepted she will join a professorial line-up that includes Lord David Puttnam and the designer Peter Gorb.
Course director Jeremy Woods said the nomination will go before the institute's professorial awards committee, headed by rector Sir Michael Bichard, early next year.
'If accepted the award should be made by May next year,' Woods said.