Real's failure to reach the last eight of the Champions League for a sixth successive season has increased the pressure on current coach Manuel Pellegrini.
The current La Liga leaders were knocked out by Lyon on Wednesday after only being able to draw 1-1 in the second leg in France, so crashing out on a 2-1 aggregate scoreline.
Real tried to lure Wenger to the Bernabeu last summer before appointing Pellegrini and the Gunners boss is in no rush to move to the Spanish capital.
He said: "Leave me alone. I am always going to stay to the end of my contract and I am going (to stay at Arsenal) until 2011. There is no way I am going to break it.
"For me, it is the worst possible moment to come back on that. At the moment my focus is fully on Hull City (on Saturday). They may be less glamorous than Real Madrid, but they are much more important in my life at the moment.
"It shows that £240million does not necessarily buy you the Champions League and that in Europe you have no guarantee of success.
"If you can spend that kind of money every year, you will get there in the end, but at the moment it is difficult for them to take.
"In the last five years we have been in the final, a semi-final and two quarter-finals in England. We don't rate that as an achievement anymore because we are used to it, but that consistency is not easy to achieve."