Pellegrini is delving into the summer transfer window and wants to tie a deal down for a tough tackling, defensive midfielder.
The 27-year-old has impressed in the Premier League since he arrived at Newcastle in 2010 and has attracted the interests of Manchester United and Arsenal in the past.
According to the Daily Mail, City are prepared to take a risk on the Ivory Coast international after Pellegrini was impressed with his performance against his side earlier in the season.