If we are really signing a marquee player, what are arguments against signing Harry Kane? All I see is that he would be a better fit for us than Griezmann(Not saying Griezmann would not help us). Kane is an out and out striker that we need. Griezmann is kind of a second striker. Kane is probably the only world class English player at the moment(Yes, he is world class imo and probably going to be the England captain someday). He has one of the best finishings if you ask me. Has proved in the premier league. Also, if you take last 3 years record, Kane is up there with some of the European elite strikers in the number of goals scored. That is not a one season wonder. Doing the same thing for 3 consecutive seasons do proves that the guy is talented. Also, he is built big and can hold the ball(Jose Mourinho's type striker). Kane has scored more goals than Griezmann has in the last 3 years. He might come for cheaper price than Griezmann too. I think serious arguement can be made on why Kane would be a better option than Griezmann.

Edit: Also, once Rooney and Carrick leaves, we won't have any reputed English players in the squad. I personally think that it is good to have some reputed English players in the core of the squad.