If Sanchez wanted to join City no matter what - we'd either sign him or there would be a bunch of negative talk from Arsenal about not trading him whatsoever. Maybe there would be some false trade rumors on Arsenal's side hoping to drive up Sanchez's price prior to sale for us.
What seems to have happened is that Sanchez said to Pep that I want to join City. Pep set this in motion in the summer and it fell through due to incompetence by Arsenal; but, we had agreed wages with Sanchez.
Now, in the Winter window, it appears as if Sanchez wants to sweeten his Manchester City deal or is willing to join another club. In other words, Sanchez is backing away from his previous commitment on wages and/or intent to join City.
And that's the red line.
If you don't want to join City, we're not interested in you.
If you agree to wages, that's it - we'll go all out for you given your promise of joining us for these wages.
Screw with us after your promise - we're no longer interested.
Sanchez is screwing with us - and thus is not a man of his word. That's the red line for Pep. He'll not be a member of our squad.
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And probably we dodged a bullet - Sanchez is skilled for sure, but is getting past his prime.
He's not well liked by players/management at Arsenal currently - so, if he doesn't get his way with regards to playing time/whatever - there's trouble brewing.
On top of all this - he's a luxury - we're currently OK in the winger/striker department - center back is probably our biggest need plus a holding mid to take over for Fernandinho once he's too old.
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TL/DR - Sanchez is a luxury signing which would improve our squad. But if he's going to dick around for wages having previously agreed terms - and if he's a potential dressing room liability - pass.