Forecasting influenza in a timely manner aids health organizations and policymakers in adequate preparation and decision making. However, effective influenza forecasting still remains a challenge despite increasing research interest. It is even more challenging amidst the COVID pandemic, when the influenza-like illness (ILI) counts are affected by various factors such as symptomatic similarities with COVID-19 and shift in healthcare seeking patterns of the general population. Under the current pandemic, historical influenza models carry valuable expertise about the disease dynamics but face difficulties adapting. Therefore, we propose CALI-Net, a neural transfer learning architecture which allows us to 'steer' a historical disease forecasting model to new scenarios where flu and COVID co-exist. Our framework enables this adaptation by automatically learning when it should emphasize learning from COVID-related signals and when it should learn from the historical model. Thus, we exploit representations learned from historical ILI data as well as the limited COVID-related signals. Our experiments demonstrate that our approach is successful in adapting a historical forecasting model to the current pandemic. In addition, we show that success in our primary goal, adaptation, does not sacrifice overall performance as compared with state-of-the-art influenza forecasting approaches.