keep a close eye 密切关注；密切留意

【例句】
But even with expectations of more intervention to boost the economy, investors will keep a close eye on developments in Europe.
但即便预期会有更多经济刺激措施，投资者还是将密切关注欧洲方面的动向。

As project manager, it is up to you to keep a close eye on how things are progressing.
作为项目经理，你需要密切关注事情的进展。