John McDonnell told an audience in Manchester the party was ready to "look again" at the free movement of people within the EU to ensure workers' rights were not undermined.
Asked about his own position during a visit to South Yorkshire, Jeremy Corbyn declined to go as far.
He said: "The European Union actually depends on the movement of people across the continent. My concerns about the way in which employers have systematically damaged working conditions across Europe and that's why I have called for this Labour market reform."
Mr Corbyn was answering questions following a speech at the Advanced Manufacturing Research Centre, in Rotherham, where he urged voters to blame politicians and big business rather than immigrants for the problems they face.
New polling suggests immigration has now become the number one issue among voters ahead of next week's vote on Britain's membership of the EU.
Mr Corbyn said: "What this referendum campaign is showing more than anything is politicians have failed and are failing to come up with solutions to the problems people face across Britain.
"The insecurity of work, the lack of good well-paid jobs, the high cost of housing whether to rent or buy, the failure to ensure decent economic growth in all parts of the country in which we can all share - it's a failure not of the EU or of EU migrants for that matter."