In the same vein as when SNL attributes fake reviews by major publications to promote fake movies and books in taped skits. For example, if I say "New York Times calls it 'the poor man's Old Man and the Sea'," to promote a humorous piece, which is not necessarily fiction or satire itself, and the fake reviews is so ridiculous that nobody would mistake it as a real review (one can hope, given what people believe in now), is it legal and/or ethical with or without a disclaimer?
"The New York Times" is a trademark. The name of any other "major publication" is highly likely to be a trademark. Using someone else's trademark, without permission, to promote your own work (or the work of a third part) is trademark infringement, or it can be.
If the satire is so obvious that no reasonable person could be confusing into thinking that the NYT is actually reviewing the work, then that is probably not infringement, but many companies have no sense of humor about their trademarks. Doing this could well cause you to get a "cease and desist letter" from the tiems or a law firm on their behalf, and if you don't stop could cause them to sue. You might win on the grounds that the fake was obvious, but you would likely incur significant costs along the way.
A statement that this was a fake review, not actually published by the Times, and that you don't own the trademark and aren't affiliated or endorsed by its owner might help in arguing that no one could have been confused, and might avoid a suit.
By the way, looking at the "trademark" tag over on Law.SE will give lots of answers on topics relates to this.