The business is up for grabs after incumbent agency Brands2Life resigned the account.
The brief, which includes media relations, is thought to be worth about £250,000 annually.
UK PR manager Jackie Nixon confirmed that a pitch process was under way, adding that 'the list is closed'.
Brands2Life is not repitching, but will be taking over Cisco's European work from Harvard PR at the start of the next financial year.
Brands2Life MD Giles Fraser said that he had resigned the UK account in order to focus on this Europe-wide work.