Under the plans, pupils would apparently be taught remotely at home for the week after half-term.
The city has the third highest infection rate in the country with 660 cases per 100,000 per population in the week up to October 11. This is behind Nottingham, which has 892, and Knowsley with 688, according to Public Health England data.
Mr Anderson earlier claimed in a tweet that Boris Johnson’s “deadly dithering has caused untold grief”.
The Labour mayor also called a “circuit breaker” lockdown to help prevent the virus spreading.
He told the BBC that the “virus was out of control” in the city, with “30 deaths” in the past seven days.
“We need to take serious action, we’re in a real battle with Covid-19,” he said. “I know it can cause disruption to parents but at the same time our teaching staff are under huge pressure.
“We have got thousands of people in the teaching profession who are isolating at the moment as well as pupils.”
Mr Anderson said it was a “very anxious” time in Liverpool and the “virus had run out of control” with hospitals under huge strain, too.
He added he would consult with other council leaders across the city region over the proposal for an additional week’s school holiday at half-term.
Damian McNulty, from the NASUWT teachers’ union, also told the broadcaster that they supported the second week, saying it was needed as a “circuit breaker” since teaching staff and pupils had been “very stressed”.
The “crisis” of the test and trace system had seen schools conducting their own tracing when children were ill and sent home “on a daily basis”, he said.