Most likely, no. In your situation (nephew living with you), he would have to qualify as your dependent. And that's unlikely if he files his own taxes.*
The main requirements for Head of Household are: a taxpayer that
1) is single or did not live with their spouse at any time during the last half of the tax year.
2) has at least one closely related dependent (usually a child) that lived with the taxpayer for more than half the year
3) pays over half of the support of the household expenses, including rent / mortgage, utilities, food.
https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9
*It's possible that he may still qualify as your "qualifying child" dependent.
There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.
The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.
A child closely related (nephew qualifies) to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support
- He lived with the relative (including temporary absences) for more than half the year
- He is younger than the relative (not applicable for a disabled child)
- If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
- If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
