Asparagus is a leading source of glutathione. Foods like broccoli (2), avocado and spinach are also known to boost glutathione levels. Raw eggs, garlic and fresh unprocessed meats contain high levels of sulphur-containing amino acids and help to maintain optimal glutathione levels. 5.oods like broccoli (2), avocado and spinach are also known to boost glutathione levels. Raw eggs, garlic and fresh unprocessed meats contain high levels of sulphur-containing amino acids and help to maintain optimal glutathione levels.