The party's former minister for Europe and chairman of the influential Home Affairs Select Committee said that Labour leader Ed Miliband's stance on the issue is softening.
"They (party leadership) have already changed their position from being a situation of 'never' and never being on the agenda to a position of 'not now' and 'we will look at it in the future'.
"That's a big change already," Vaz told the Evening Standard.
The Leicester East MP predicted that all three major parties in Britain - coalition partners Conservatives and Liberal Democrats, and Opposition Labour - will pledge in their next manifestos to allow a vote on whether to stay in or quit the EU, which could neutralise Prime Minister David Cameron's landmark referendum pledge as a general election issue.
"The problem is the entire debate is conducted by those who are opposed to the EU," Vaz added.
The MP has led Labour's pro-EU wing since 1999 when, as Europe minister, he toured the UK in a bus to promote Britain's relations with the EU.
Now he is leading a group of Labour MPs and front-benchers who believe Miliband must match the Tory promise of a referendum.
Vaz feels Cameron has set himself an "impossible" target of negotiating major EU reforms in time for a referendum in 2017, after the next general elections scheduled for 2015.
Meanwhile, the British PM is facing immense pressure from within his own Tory party to bring forward an in-out referendum as the anti-EU sentiment gathers ground within the political circles in the UK.
Cameron's authority suffered a huge blow when more than 100 of his party MPs defied him by voting for a referendum on the EU today.
Although the amendment was defeated by 277 votes to 130, 114 Tory MPs voted in favour of it marking the biggest backbench revolt on Europe since the 2010 election.
Britain seemed to move closer to an in-out referendum as Deputy Prime Minister Nick Clegg told MPs: "It is a question of when, not if, because the rules [of the EU] are bound to change.
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