“We will hear more about it, I believe, over this week”
Senior figures close to Mr Corbyn said he could announce his backing of the controversial vote in the next few days.
It comes after millions chose to cast their ballots for Remain-backing parties the Greens and Liberal Democrats over Labour in the EU elections last week.
The party — along with Theresa May’s Conservatives —was totally humiliated in the vote, coming third overall behind the Lib Dems and the no-deal-supporting Brexit Party, which secured the most votes.
Mr Corbyn has so far refused to throw his weight behind another vote on leaving the EU despite having come under pressure from his members to take a pro-Remain position.
The party’s unwillingness to strongly take up a Leave or Remain position is likely due to its voter base, which was split between the two options in the 2016 referendum.
But, Welsh Labour leader Mark Drakeford, who said he spoke to Mr Corbyn this week, has now said the party could finally leap into the Remain camp.
Mr Drakeford added: “He continues to get advice from a variety of different sources. I think the UK position is still evolving.
“We will hear more about it, I believe, over this week.”
Shadow Home Secretary Diane Abbott, a member of Mr Corbyn’s cabinet, said: “We’re supporting a people’s vote strongly now because it’s the right thing to do and it’s democratic.
“There is no inherent contradiction between respecting the result of the referendum and having a people’s vote, not least because it’s still not sure how a people’s vote would pan out.”
Another senior Shadow Cabinet minister added: “We need to be more definitive quickly and you’ll see that in the next couple of days, to give our membership confidence again that they can get back on the doorstep because they couldn’t this time around.”
Labour took 10 seats and only managed to squeak a dismal 14% of the vote, well behind Nigel Farage’s Brexit Party which romped to a solid victory and nabbing nine of 12 UK regions.
The Tories also suffered a humiliating night, with many former supporters growing frustrated that the UK failed to leave the EU on March 29.
Prime Minister Theresa May delayed the departure and a new leave date has been set for October 31 this year.