City have been knocked out in the group stages in both their Champions League campaigns to date.
According to Goal.com, the club's hierarchy have added this incentive to help the team progress this year.
Pellegrini took Malaga to the brink of the semi-finals last season, and is tasked with improving City's form in Europe.
It is thought that City could target players from clubs who have been knocked out of the competition by January, with the defence being identified as an area in need of improvement.
City have already spent over £90m so far this summer.