Both men started the Red Rose's 21-8 victory over Argentina in their opening match of the Autumn Internationals on Saturday afternoon - a result and performance that left Jones visibly upset in the stands.
Woodward believes that Jamie George, who came off the bench against Los Pumas, deserves to start at hooker against the Wallabies, with skipper Hartley and Ford seen as the weak links in the side.
"I want to see what [George] can do. I think he should have started the game against Argentina," he told Sky Sports News.
"I think George and Harry Williams are really knocking on the door against Hartley and Dan Cole, which means a change of captain, but I think we have got to have that change. Samoa will be too late so we've got to find out."