See below from the FAQs (children section) for citizenship. He will need ILR as born abroad.
born abroad
If the child was born outside the UK, then once one parent applies for naturalisation, the child can apply for Registration under section 3(1). The is application at discretion and the HO would expect that the other parent to hold (or to be close to holding) a ILR/PR status.
For the guidelines on Registration at discretion see section 9.17 .
Q3: I’m due to apply for ILR. Can I skip applying for ILR for my child?
If the child is UK born, then he can apply for registration as BC once one parent is granted ILR, irrespective of immigration status so ILR application can be skipped. However, the process of applying + passport application can take 3-6 months so if there are plans for the child to travel during that period, he will require a suitable visa to re-enter the UK. In that case, you should not skip the ILR.
For children born outside the UK, ILR is normally required.
http://www.immigrationboards.com/viewtopic.php?t=95747