Daniel Pelka, from Coventry, died in March 2012, after being starved and abused by his mother and her boyfriend.
Speaking in the wake of a four-week Ofsted inspection of the service, Brian Walsh, of the city council, said he was "very concerned" about the results.
The Ofsted report is due out later this month.
In September, a serious case review found he was "invisible" at times to police, NHS and social care.
Since Daniel's death, the council said referrals have risen from 3,085 in March 2013 to 4,529 in March 2014.
Mr Walsh, who took over the department in September, said: "I am very concerned about what Ofsted are going to say.
"The increase in referrals has completely overwhelmed us in social care."
However, Mr Walsh added Coventry's child protection services were "very different" to those in Birmingham which were branded a "national disgrace" by Ofsted's chief inspector Sir Michael Wilshaw in October.
Ofsted has rated Birmingham's children's services inadequate since 2009 and the latest inspection was cancelled to allow a government review into the authority's plans to improve the department.
Mr Walsh said: "We are in a very different position to Birmingham. We are a much smaller authority and we are aware of the problems. We will welcome external support if that's what's required."
The head of the social care department that "missed chances" to save the life of a four-year-old boy said his team has been "overwhelmed" by cases.