British media have cited pictures posted online by the militants, which say Abu Yusuf al-Britani took part in a suicide attack in Iraq's Salahuddin province.
He is believed to be Talha Asmal, a teenager who left West Yorkshire in March, and was thought to have joined Islamic State, according to a statement from his family.
"Although the information within these reports has not been confirmed and the relevant UK authorities are working hard to verify the facts, we can confirm that the photographs shown of a youth purportedly named Abu Yusuf al-Britani appears to show our 17-year-old son Talha," the family of Talha Asmal said in a statement issued by West Yorkshire police on Sunday.
"We are all naturally utterly devastated and heartbroken by the unspeakable tragedy that now appears to have befallen us."
Security services have estimated that at least 600 Britons have gone to Syria or Iraq to join militant groups, including the man known as "Jihadi John" who has appeared in several Islamic State beheading videos.
Hundreds of other Europeans have also joined the fight.
The family said Asmal came from a close knit, hardworking, peace loving and law abiding British Muslim family, and the entire family unreservedly condemned and abhorred all acts of violence wherever they were perpetrated.
West Yorkshire police said they were aware of the reports, but were unable to comment further as the person's identity had not been confirmed.
According to media reports, Islamic State said 'al-Britani' was one of four suicide bombers - with the others said to be a German, a Kuwaiti and a Palestinian - who took part in the attack.
Islamic State controls swathes of territory in eastern Syria and northern Iraq where it has declared an Islamic caliphate.
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