This paper presents a deep learning-based method for predicting signal to interference and noise ratio (SINR) in direct-to-device low earth orbit (LEO) satellite communication under inter-constellation interference. The rapid mobility of LEO satellites causes severe SINR fluctuations, while large propagation delays lead to outdated measurements. These effects, combined with inter-constellation interference, make accurate SINR prediction essential for reliable satellite communication. To this end, we first emulate SINR dynamics with inter-constellation interference scenario, and propose a noise-adaptive Kalman filter (KF) as a model-based baseline. Since its performance is limited for multi-step prediction, we introduce lightweight recurrent neural network (RNN)-based models, including long short term memory (LSTM), gated recurrent unit (GRU), Bidirectional LSTM (BiLSTM), and an encoder–decoder LSTM. Simulation results show that the proposed models significantly outperform the KF, particularly in multi-step prediction, demonstrating their ability to capture temporal correlations in interference-limited satellite channels and enabling practical link quality prediction in non-terrestrial networks (NTNs).