Elena Narozanski stopped working as one of the Education Secretary's special advisers about a month ago, but it is thought that Gove is planning to bring her back as a civil servant on a £42,000 wage.
The department advertised two speechwriter roles in The Guardian, calling for people 'to craft compelling, convincing speeches to communicate government policy'.
The roles have already attracted negative coverage in the media for dodging the civil service recruitment freeze.
PRWeek understands it is open knowledge within the DfE comms unit that Narozanski is being lined up for the role.
A DfE insider said: 'Gove is trying to bring in his own woman to do this job. He knows exactly who he wants. There's a bigger story behind this - he has lost control of his department and is desperately trying to reassert it, but of course things such as this just backfire.'
In what may be interpreted as a step towards building up a more focused comms unit, Gove has appointed James Frayne as director of comms. He starts in April. Currently a partner at Westbourne, Frayne formerly worked at the TaxPayers' Alliance, which has links to the Conservative Party.
Dominic Cummings, Gove's former chief of staff, was also brought in as a second special adviser this year.
A DfE spokesman said he was not aware Narozanski was being considered, adding that 'anybody who applies will be considered'. The deadline for applications is 21 March.