The clause backing "common ownership of the means of production, distribution and exchange", was scrapped under Tony Blair in 1995.
Speaking to the Independent on Sunday, Mr Corbyn said Labour "shouldn't shy away" from public control of railways and public investment in industry.
Leadership rival Liz Kendall told the paper Clause IV belonged in the past.
Tony Blair's move two decades ago to ditch the long-standing commitment in Labour's constitution to public ownership was seen by some as a symbolic step which made the party more electable in the post-Margaret Thatcher era.
The original wording of Clause IV was replaced with a new commitment to "a thriving private sector and high-quality public services where those undertakings essential to the common good are either owned by the public or accountable to them".
Mr Corbyn told the IoS he could consider bringing back the old Clause IV as part of a commitment to take "necessary things" back into public ownership.
"I think we should talk about what the objectives of the party are, whether that's restoring the Clause IV as it was originally written or it's a different one, but I think we shouldn't shy away from public participation, public investment in industry and public control of the railways," he said.
"I'm interested in the idea that we have a more inclusive, clearer set of objectives. I would want us to have a set of objectives which does include public ownership of some necessary things such as rail."
Mr Corbyn's campaign momentum seems unflagging  - to the alarm of senior figures in the party. But he says the party needs a new statement of objectives - and that could be the original Clause IV.
Jeremy Corbyn has already promised to renationalise energy companies and the railways and increase public spending on industry. One of Mr Corbyn's leadership rivals, Liz Kendall, condemned the idea as a "throwback to the past".
Some party donors are alarmed by the prospect of a Jeremy Corbyn win too. Businessman Assem Allam, who donated Â£300,000 to Labour during the election, has told the Sunday Telegraph he would stop giving money to the party if Mr Corbyn becomes leader, saying he never backed a "dead horse".
Mr Corbyn is one of four candidates standing in next month's Labour leader election, alongside Liz Kendall, Yvette Cooper and Andy Burnham.
Ms Kendall - the leadership challenger seen as being the closest to Mr Blair's policies - fiercely condemned the idea of bringing back Clause IV.
"This shows there is nothing new about Jeremy Corbyn's politics," she said.
"Life had moved on from the old Clause IV in 1994, let alone 2015. We are a party of the future, not a preservation society."
At-a-glance profiles of the four contenders

McDonald's planned to open a two-storey restaurant in Fishponds in 2014.
There was fierce opposition from a campaign group over congestion and childhood obesity concerns.
The planning inspector said there was little evidence the "proposal would result in any significant increase in obesity".
Mike Jempson from the Say No To McDonald's campaign group said he was "appalled and astounded" by the decision, which he claims was taken "with scant regard to the wishes and concerns of local residents".
He said: "Disgracefully, he [the inspector] dismisses the 495 written objections received by the council, the 1,667 signatories to the No McDonald's In Fishponds petition, and 617 signatures of families in the streets most directly affected by the scheme."
He added that the group will consider its options before deciding whether to challenge in the High Court.
A McDonald's spokesperson said: "We are pleased that our application has been allowed but will now be taking time to review the inspector's decision.
"We strongly believe that we will make a positive contribution to the local community, not least through the creation of 65 new jobs for local people."

The 29-year-old made 37 appearances for the Sky Blues last season as they were relegated from League One.
Reid, who has also had spells with Charlton, Bradford and Preston, could make his debut for the U's in Wednesday's EFL Cup first-round tie against Championship side Aston Villa.
Colchester started the season with a 3-1 defeat at Accrington on Saturday.
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Jeremy Corbyn has said Labour could restore Clause IV committing it to public ownership if he became leader.
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The government has overturned a decision by Bristol City Council to refuse planning permission for a McDonald's drive-through.
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Colchester United have signed winger Kyel Reid on loan until January from League Two rivals Coventry City.