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According to reports from The Telegraph, Robinson will be appointed as manager of Oxford's League One rivals, Bromley.
The Ravens currently sit bottom of the table with just two wins and nine points after winning promotion from League Two last season.
Former England and Tottenham Hotspur striker Jermaine Defoe is reportedly set to join the ex-Yellows boss as his assistant.
Robinson's first game will be an FA Cup tie with Rotherham United, who are managed by his former assistant Alex Bruce.
The job will be Robinson's fifth in the EFL.
The 46-year-old has been out of work since leaving Salford City in June following their 3-0 play-off final defeat at Wembley against Notts County.
According to the Daily Mail, Matt Bloomfield was also considered for the Bromley job.