Type 1 Diabetes Mellitus (DM1) patients are used to checking their blood glucose levels several times per day through finger sticks and, by subjectively handling this information, to try to predict their future glycaemia in order to choose a proper strategy to keep their glucose levels under control, in terms of insulin dosages and other factors. However, recent Internet of Things (IoT) devices and novel biosensors have allowed the continuous collection of the value of the glucose level by means of Continuous Glucose Monitoring (CGM) so that, with the proper Machine Learning (ML) algorithms, glucose evolution can be modeled, thus permitting a forecast of this variable. On the other hand, glycaemia dynamics require that such a model be user-centric and should be recalculated continuously in order to reflect the exact status of the patient, i.e., an ‘on-the-fly’ approach. In order to avoid, for example, the risk of being disconnected from the Internet, it would be ideal if this task could be performed locally in constrained devices like smartphones, but this would only be feasible if the execution times were fast enough. Therefore, in order to analyze if such a possibility is viable or not, an extensive, passive, CGM study has been carried out with 25 DM1 patients in order to build a solid dataset. Then, some well-known univariate algorithms have been executed in a desktop computer (as a reference) and two constrained devices: a smartphone and a Raspberry Pi, taking into account only past glycaemia data to forecast glucose levels. The results indicate that it is possible to forecast, in a smartphone, a 15-min horizon with a Root Mean Squared Error (RMSE) of 11.65 mg/dL in just 16.15 s, employing a 10-min sampling of the past 6 h of data and the Random Forest algorithm. With the Raspberry Pi, the computational effort increases to 56.49 s assuming the previously mentioned parameters, but this can be improved to 34.89 s if Support Vector Machines are applied, achieving in this case an RMSE of 19.90 mg/dL. Thus, this paper concludes that local on-the-fly forecasting of glycaemia would be affordable with constrained devices.