The Premier League champions are reportedly willing to spend big in the January transfer window, and the Real Madrid pair are thought to be top of Manchester City's transfer wishlist.
Big-spending French side Paris St-Germain are expected to move for Ronaldo as well, and with the future of Real Madrid boss Jose Mourinho currently uncertain, the Ligue 1 club are believed to looking to make the most of the situation to lure the Portuguese striker to the Parc des Princes.
Sources in Portugal, quoted by Portuguese newspaper O Jogo, claim that City are ready to bid up to £134m in an effort to land the duo.
But Roberto Mancini could find it difficult to convince Ronaldo to join City, as the former-Manchester United star spent six hugely successful years at Old Trafford.
Real Madrid paid United £80m for the Portugal star's services in 2009, and Ronaldo has gone on to average a goal a game since joining - he already has 14 La Liga goals this term.
But, if the report is correct, Madrid stand to make a tidy profit on Ronaldo and Coentrao, who joined the La Liga champions from Benfica in 2011. Both players are Portugal internationals, and featured as Paulo Bento's side reached the semi-finals of Euro 2012.