// Singleton class
class Singleton
{
  private static Singleton instance;
  public static Singleton Instance
  {
    get
    {
      if (instance == null)
        instance = new Singleton();
      return instance;
    }
  }

  public GameObject Player { get; set; }
}

// Attached to player
class Player: MonoBehaviour
{
  Awake()
  {
    Singleton.Instance.Player = this.gameobject;
  }
}

// Now you can call Player from anywhere:
var player = Singleton.Instance.Player;