Some work in that direction, including an elaborate example, can be found at http://www.sciencedirect.com/science/article/pii/0304407695017445

AIC is one of a few criteria to select models, typically in multiple regression studies.  In the selection process, models with similar AIC values may have different sets of variables.  Other characteristics of the competing models should be taken into consideration to shortlist the favourite model.  Assuming there are no complications with the elected model, that is, diagnostics show no violation of assumptions, the importance of the variables in the "best" model can be seen by their respective P-values; loosely, this is also reflected in the correlation coefficient with the dependent variable.    

Bibliography:

DRAPER, N.R.  and  SMITH, H.  1981.  Applied Regression Analysis.  Wiley.

MONTGOMERY, D.C.  and  PECK, E.A.  2007.  Introduction to Linear Regression Analysis.  John Wiley & Sons.  

MYERS, R.H.  2000.  Classical and Modern Regression with Applications.  Duxbury Press. 

Thanks Victor, can you elaborate it by giving an example !!

Hi Rahul,

I'm not quite sure whether I understand your question correctly, but I'll try to explain....

The AIC does not give you results which can be interpreted directly. It just gives you a hint which model you should apply given a set of candidate models. Like common for these information criteria, it takes the log-likelihood of the model as accuracy measure on the one hand but punishes for the inclusion of many exogenous variables into the model. The AIC is therefore in my opinion the wrong measure regarding your question. The p-value is not really a correct measure for the importance of the variable either. It just tells you with which probability the respective variable indeed is correlated with your dependent variable.

You COULD take the likelihood of the unrestricted model and compare it to the likelihood of the restricted model leaving one of the explanatory variables out. This would give you the "relative loss in accuracy" due to omission of the variable.

E.g. calculate the Likelihood of model M1, leave variable X out (M2). Instead leave variable Y out in the next step(M3). If the likelihood in M2 is bigger than the one in M3, you know that Y is "more important" than X.

Not textbook-based, but I would handle this by intuition if your aim is to understand this thing.

Best regards!

Download my papers about CPD data. There are many examples.