Can a cancerous breast lump ever have oozing or weeping?

Very Rarely: Oozing or weeping from the skin of the breast is most commonly due to a skin-based infection rather than a breast (tissue) disease. However, a large cancer can erode through the skin and cause an open, oozing wound. Also, a rare from of cancer, inflammatory breast cancer, can mimic a breast infection with skin changes. In short: it's best to see your doctor just to be safe.