Not trying to be offensive but do you think that a lot of big players (especially ones coming from other leagues) turn down Liverpool because...well it means living in Liverpool.
I've heard plenty of times that players prefer to play for a team in London because of the city itself and not necessarily the club. I know your fans bark on about history a lot but that's not really as big a factor to players nowadays as it once was.
In the last year alone you've been overlooked by Salah, Willian and Sanchez who have gone to London based teams.