Allardyce said: "Chelsea did it when Roman Abramovich came in and I have no doubts City could do the same.
"City look like they are intent on getting to that level and if the spending is on the same level of Abramovich then I am quite sure they will have a major impact.
"All of a sudden they are under threat. They have been in the top four so long that each year they have been able to set their budget in advance because they know they will be in the Champions League. Now that could all change. And if City do take one of their places it could be catastrophic financially because it could cost them £25m or more if they aren't playing in the Champions League."