Manning’s current club Bristol City confirmed that the 39-year-old would take a break from football, with his assistant Chris Hogg, who was also his number two at United, set to take charge for the foreseeable.
The Robins are currently 16th in Sky Bet Championship and won 2-1 at home against the U’s last month.
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“Everyone at Bristol City Football Club is deeply saddened by the passing of Liam’s recently born son Theo John Manning,” the Robins said in a statement.
“We know that Bristol City’s supporters and the wider football family will share their condolences and deepest sympathy with Liam, his wife Fran and his son Isaac during this difficult period.
“Liam will take a period of absence, and all football duties will be carried out by Chris Hogg.
“We ask that the privacy of Liam and his family is respected during this time.”
Manning left United for the Robins in November last year, having took over the U’s in March.
He guided United to safety in League One at the end of the 2022/23 campaign, and when he exited early on during the following season, the U’s sat second in the table.
United said in a statement: “Everyone at Oxford United is deeply saddened by the passing of Liam Manning’s recently born son, Theo.
“We send our deepest condolences to Liam, his wife Fran, and their son Isaac during this incredibly difficult time.
“The whole Oxford United family and community of supporters is behind you, Liam. We are always United.”