Gunners boss Arsene Wenger's job was in question earlier this term but Hodgson always knew that the Frenchman would get things on track after a slight miscue.
"Are Arsenal back? Have they ever been away?" he said.
"There was all the stuff about Arsene being under the spotlight and pressure.
"I think all managers at this level will accept they come under the spotlight and pressure if your team isn't winning as many games as people would like to see you win.
"But I would find it very hard to believe if Arsenal FC were considering Wenger's future because for the last 15 years he has done a fantastic job.
"He has proved himself to be one of the best managers in the world and has made that club an enormous amount of money when other clubs are losing money and staring administration in the face.
"He has made that club stronger and stronger, richer and richer. His list of achievements just goes on and on."