I heavily doubt this rumour and can't see Lambert letting him go in January. City don't need to spend the money and Pilks will be a key player to keep us in the PL. I would also think that any other team would like to see him play more than 12 games in the PL before splashing out the money.
Liverpool do have a history of splashing the cash on lower league or lesser thought of players. They paid nearly 2M for Shelvey who hadn't played higher than L1.