The publication of tourism statistics often does not keep up with the highly dynamic tourism demand trends, especially critical during crises. Alternative data sources such as digital traces and web searches represent an important source to potentially fill this gap, since they are generally timely, and available at detailed spatial scale. In this study we explore the potential of human mobility data from the Google Community Mobility Reports to nowcast the number of monthly nights spent at sub-national scale across 11 European countries in 2020, 2021, and the first half of 2022. Using a machine learning implementation, we found that this novel data source is able to predict the tourism demand with high accuracy, and we compare its potential in the tourism domain to web search and mobile phone data. This result paves the way for a more frequent and timely production of tourism statistics by researchers and statistical entities, and their usage to support tourism monitoring and management, although privacy and surveillance concerns still hinder an actual data innovation transition.