The move comes after the redeployment of comms officer Eileen Short, sister of Labour MP and former cabinet member Clare Short.
Contrary to its policy of not commenting on individual staffing issues, the east London authority issued a written statement to PRWeek.
Assistant chief executive Sara Williams, who has responsibility for comms, denied that the council had victimised Short.
The statement said: 'We are satisfied that employment procedures have been followed. Short is on the redeployment list following a reorganisation earlier in the year in which she was not successful in securing a post.'
The council is also concerned that coverage of the potential strike has presented a distorted picture.
It now has three months to redeploy Short, who faces redundancy if the process is unsuccessful.
The review is being implemented by retained agency Verve Communications, which replaced Tribal MPC in August. Verve MD Lorraine Langham said: 'We hope council staff do not go on strike as it's an exciting borough with a positive story to tell, and we want to work with them to get that message across.'
Verve is providing strategic support and interim cover for a number of vacancies, including the head of comms post, held by freelance
consultant Don Neame.
Speaking on behalf of Short, the Tower Hamlets branch secretary of Unison, Jean Geldart, said: 'What the council is saying is nonsense. There are four press-facing posts to which Eileen could be deployed but it is refusing to offer her one of them.'