I'm sorry that your question wasn't answered in a timely manner. I would need to needle aspirate that mass and examine the aspirate microscopically to be able to tell you what the mass represents because birds can develop quite an assortment of masses. A xanthoma - a fatty-cholesterol-laden mass, however, is one of the more common masses appearing in the area you've described.
If, indeed, a xanthoma is present, some birds will respond to nutritional therapy. Often these birds are on high fat, all seed diets. Weaning slowly onto a balanced diet (pellets + fruits and vegetables) plus supplementation with vitamin A or vitamin A precursors may be successful. If the xanthoma continues to enlarge, or becomes ulcerated, bleeding, infected or painful, surgical removal is required. If the mass is left untreated, it may become large enough to impair the bird's movements. In addition, the bird becomes susceptible to sudden bleeding episodes and may bleed to death.
The goal of surgery is to completely remove the xanthoma and any surrounding fatty, necrotic or ulcerated skin. The more complete the excision, the less likely the tumor will recur. Sometimes the tissue so diffusely infiltrates areas of surrounding skin that surgical excision may be incomplete; in these cases, the mass will be "debulked" as much as possible. In some cases, the xanthoma is so large that to remove it all would not leave enough healthy skin to close the surgical wound. Suturing incompletely removed xanthomatous tissue is complicated by the fact that the tissue is weak and may not hold the sutures well.
Please respond with further questions or concerns if you wish.