Can I impute an independent variable with a dependent varible?

#1
I'm building a regression model

Y = X1 + X2 + ... + Xn

There're about 10% subjects who have missing value on two of the predictors. If I use multiple regression method to impute these two variables, can I include Y as a predictor? If I do so, am I doing analysis in circles? i.e., using Y to predict X and then using imputed X to predict Y? It feels strange. Can someone help please?

Thank you!
 
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