Talha Asmal, 17, was one of four suicide bombers who attacked security forces near an oil refinery south of Baiji, The Guardian has reported.
Isis social media reports said Asmal, going by the name of Abu Yusuf al-Britani, had taken part in the attack.
His family said they were "devastated" at the news.
Asmal, from Dewsbury, would be Britain's youngest known suicide bomber. Another West Yorkshire teenager, Hasib Hussein, was almost 19 when he blew himself up on a London bus in the 7 July 2005 attacks.
A statement issued by Asmal's family said: "Talha was a loving, kind, caring and affable teenager.
"He never harboured any ill will against anybody nor did he ever exhibit any violent, extreme or radical views of any kind.
"Talha's tender years and naivety were it seems however exploited by persons unknown who, hiding behind the anonymity of the world wide web, targeted and befriended Talha and engaged in a process of deliberate and calculated grooming of him.
"Whilst there it appears that Talha fell under the spell of individuals who continued to prey on his innocence and vulnerability to the point where if the press reports are accurate he was ordered to his death by so-called Isis handlers and leaders too cowardly to do their own dirty work.
"We are all naturally utterly devastated and heartbroken by the unspeakable tragedy that now appears to have befallen us."
West Yorkshire Police said: "The police have been made aware of media reports with regard to the death of a British National in Iraq.
"The identity of the person who has reportedly died has not been confirmed at this time and we are unable to comment further."
Asmal travelled to Syria with fellow Dewsbury teenager Hassan Munshi.
Munshi's brother, Hammaad Munshi, was arrested in 2006 at the age of 16 after police found a guide to making napalm on his computer.
He became the youngest person to be convicted under the Terrorism Act.
At least 700 people from the UK have travelled to support or fight for jihadist organisations in Syria and Iraq, British police say. A BBC News database tracks those who have died, been convicted of offences relating to the conflict or are still in the region.

In a match reduced to 17 overs per side at Old Trafford, only seven were possible with Lancashire on 39-0.
But Warwickshire's win at Yorkshire and Worcestershire's victory over Notts saw the 2014 champions finish fifth in the North Group with a worse net run-rate.
Lancashire remain bottom of the group with just two wins.
Following a delay of more than four hours, play eventually got under way at 18:15 BST with each innings reduced to 24 overs, and Lancashire's Karl Brown raced to 30 not out.
The players went off for rain 30 minutes later, but it was hoped they could start again at 19:45 BST, with the match now 17 overs for each team.
However, the weather closed in again and they did not return - meaning both sides take one point.

At least 290 people were killed and hundreds more injured when the 6.2-magnitude quake struck in the early hours of Wednesday, 100km (65 miles) north-east of Rome.
The town of Amatrice was among the worst affected areas.
The service at St Andrew's Cathedral was led by the Archbishop of Glasgow, Philip Tartaglia.
It follows a similar event in Edinburgh on Sunday.
Ronnie Convery, director of communications for the Archdiocese of Glasgow, said there had been wide interest in the service from Scotland's Italian community.
"We are looking at something like 400 new arrivals from Italy every month at the moment in Glasgow and Edinburgh," he said.
"It's those people I notice on social media who have really taken up the information about the mass today.
"It's also interesting that in many cases people are not necessarily practicing Catholics but they just want to have that opportunity to be together, to meet, to do something."
A West Yorkshire teenager is believed to have become Britain's youngest ever suicide bomber after reportedly blowing himself up in Iraq.
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Durham were eliminated from the One-Day Cup after their match against Lancashire was abandoned and other results went against them.
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A mass has been held in Glasgow to remember the victims of last week's earthquake in central Italy.