The People says Eriksson wants to bring Benzema to Eastlands in January, but will have to cough up £14 million for France's new star.
City spies will watch Benzema again this week when he plays in Europe and they will decide where to pitch their offer shortly. But it will have to be close to Lyon's valuation.
The quick, strong and skilful young attacker has a fantastic set of stats already. He has bagged 16 goals in just 50 games for Lyon since making his debut at 16.
And in the elite Champions League competition he has also claimed two goals in just six appearances, so he can mix it with the best.