The DNC will reportedly vote on the measure this week at its summer meeting in Phoenix.
At least 16 women, including city employees, have come forward to accuse Filner of sexual harassment. He denies the allegations, but earlier this month completed a two-week intensive therapy session for sex addiction.
Filner has returned to San Diego, where a recall effort is underway, but has not returned to City Hall. Reports from local news outlets said the mayor may be in the process negotiating a potential resignation agreement.