The bottom line is that while not cheap signing Sanchez now is a lot cheaper than signing Griezmann in the summer for example.
The alleged difference in wages being offered is 75k a week or roughly 4m a year. If he signs a 3 Yr contract that is 12m extra in wages. Hardly a game breaker when you consider Arsenal want 35m and any potential summer striker will be 100m.
So it is definitely about not wanting to break salary cap. If Sánchez were to wait until the summer I am sure we could give him 30m signing on fee and then his 275k a week salary.