In an emailed statement, the telecoms company said it was vital to have access to the European Union's free "movement of people, capital and goods".
They added they would "take whatever decisions are appropriate" although it was too early to "draw any firm conclusions regarding the long-term location for the headquarters".
The company is also to start reporting its financial results in euros, rather than pounds following last week's vote for the UK to leave the EU.
Sent to several media organisations, the email outlined how free movement had led to the success of their business.
Vodafone said that 55% of group profits in the last financial year came from its European operations, with the UK providing just 11%.
The company said: "It remains unclear at this point how many of those positive attributes will remain in place once the process of the UK's exit from the European Union has been completed."
The firm employs 13,000 people in the UK, with operating divisions at Newbury, Berkshire as well as the main centre in Paddington.
Vodafone is the seventh largest company listed on the FTSE 100.
Single market access is 'number one priority'
In a meeting held with business executives, Secretary of State Sajid Javed said the biggest issue was ensuring access to the free market still contined.
He said: "While I am not in any position to make promises, I assured everyone that my number one priority will be just that in the negotiations to come."
Meanwhile, in a summit held on Tuesday (June 28), London Mayor Sadiq Khan addressed business leaders and said London needed more powers "right now" to protect the city from economical downturns.