The Reds are challenging Bayern Munich for the Germany midfielder.
Sane has one year remaining on his deal with City, but Mills claims it would be difficult to ignore an offer from the Merseyside club given their success over the past 12 months.
He told Football Insider: "Clubs do not want to sell to their immediate rivals and that is normally the biggest problem.
"If Liverpool want Sane I am pretty sure he would go there given the opportunity. Why wouldn't you?