Accurate forecasting of the F10.7 index at different time scales is crucial within the framework of Space Weather thanks to the role it plays as a proxy of solar activity. F10.7 refers to the measure of solar radio emission at 10.7 wavelength, and it is utilized in various applications, such as ionosphere and thermosphere modelling, radio communications and navigation, remote sensing, and space environment modelling. The forecasting of the F10.7 index can be challenging due to the non-linear, non-stationary, and chaotic features of the underlying physical processes that generate it. To address these challenges, we present a multivariate deep learning architecture based on a Long Short-Term Memory (LSTM) network complemented by a multi-attention module. It integrates the Fast Iterative Filtering (FIF) algorithm and feature importance analysis to enhance its performance. This model takes multiple solar indices, specifically F3.2, F8, F10.7, F15, F30 and the sunspot number, as input data to predict the F10.7 index on a daily basis for up to 25 days in advance. By incorporating these additional input variables and employing data preparation techniques, the proposed method outperforms classical univariate LSTM-based models in terms of accuracy and reliability, achieving a root mean square error (RMSE) of approximately 5 sfu (solar flux units).