Bronchitis: Given the presence of cough with green phlegm in a patient with uncontrolled diabetes, bronchitis is a likely diagnosis. The green phlegm suggests a bacterial infection, and diabetes increases the risk of infections, including those of the respiratory tract. However, the absence of fever and clear chest might suggest a chronic or mild form of bronchitis.

Chronic Obstructive Pulmonary Disease (COPD): Patients with diabetes are at an increased risk of developing COPD, and chronic cough with colored sputum can be a symptom. The absence of other signs of infection and clear chest does not rule out COPD, especially if the patient has a history of smoking or exposure to pollutants.
Asthma: Asthma can cause chronic cough and sputum production. In patients with uncontrolled diabetes, the metabolic state might exacerbate asthma symptoms or make them more difficult to control.
Pulmonary Tuberculosis: Although less common, TB should be considered, especially if the patient has been exposed or has risk factors. The presentation can be atypical, especially in diabetic patients, with fewer symptoms than expected.

Pneumonia: Despite the chest being clear and no fever, pneumonia, especially if caused by atypical organisms or if the patient is immunocompromised due to uncontrolled diabetes, can present atypically. It's crucial to consider and possibly rule out with further testing if necessary.
Invasive Aspergillosis: In severely immunocompromised patients, including those with very poorly controlled diabetes, invasive aspergillosis can present with cough and sputum production. It's a life-threatening condition that requires prompt diagnosis and treatment.
Mucormycosis (Black Fungus): This rare but deadly fungal infection has been noted in patients with uncontrolled diabetes, particularly during the COVID-19 pandemic. It can affect the lungs and sinuses, presenting with cough among other symptoms.

Cystic Fibrosis: Although typically diagnosed in childhood, some cases of cystic fibrosis may not be diagnosed until adulthood. It can cause chronic cough, sputum production, and recurrent infections.
Bronchiectasis: This condition involves damage to the airways, leading to chronic cough and sputum production. It can be primary or secondary to various conditions, including infections, and might be considered if other diagnoses are ruled out.
Alpha-1 Antitrypsin Deficiency: A genetic disorder that can cause COPD-like symptoms in non-smokers. It's a rare condition but should be considered in the differential diagnosis of chronic respiratory symptoms.