Communications Minister Malcolm Turnbull lost an internal battle with Prime Minister Tony Abbott over whether businessman Joseph Skrzynski should be appointed to a second term as SBS chairman.

Fairfax Media understands Mr Turnbull lobbied strongly for the investment banker - whose five-year term expires next Wednesday - to remain in the position but was overruled by the Prime Minister's office.

Malcolm Turnbull and Tony Abbott. Credit:Angus Mordant

In a statement released on Monday, Mr Turnbull praised Mr Skrzynski as an "outstanding chairman" and said that "SBS is a stronger organisation for his leadership".

Labor leapt upon Mr Skrzynski's departure to demand the Abbott government commit to retaining a merit-based process for ABC and SBS board appointments.