Real boss Carlo Ancelotti is aiming to strengthen his Champions League-winning squad with some heavyweight additions ahead of next season.
Suarez has long been linked with Real despite the Liverpool striker claiming he is happy at Anfield, per the Daily Mirror's David Anderson:
The Madrid outfit are reportedly continuing their pursuit of the Uruguayan and will table bids for him and Brazilian Ramires, per Simon Jones of the Daily Mail.
Jones reports that Blues boss Jose Mourinho will resist any offer for Ramires, who has been of interest to Ancelotti for some time; the Italian manager enquired about his availability back in November.
Mourinho's reported interest in various Real players could play a part in Ramires' future, with a swap deal potentially on the cards.
Sami Khedira, Isco and Raphael Varane could all potentially go the other way if the Brazil international does indeed make the switch to Spain, per Ben Jefferson in the Express.
The 27-year-old midfielder played a key role for Chelsea last season, as they finished third in the Premier League and reached the semi-final of the Champions League.
Madrid are also targeting Bayern midfielder and long-term Manchester United target Kroos, who has only one year left on his contract at the Allianz Arena.
According to Spanish newspaper AS, the German international has not yet signed a contract extension, as Bayern are refusing to give him what he wants.
The 24-year-old reportedly asked his club to listen to offers for him, per Jose Felix Diaz of El Confidencial (via 101 Great Goals), having previously been convinced he would not be allowed to leave this summer, per Bild (via FourFourTwo):
I would be very surprised (if Bayern let me leave before end of his contract in 2015). The club was very clear and told me that a transfer in 2014 would not be possible. There has been much speculation, but Manchester United was never an issue and is no issue right now.
Even if Real cannot sign him this transfer window, they could potentially then pick him up for free next summer when his contract in Bavaria has expired.
The German international made 29 appearances in Bayern's Bundesliga-winning 2013-14 campaign, scoring two goals and providing four assists. He had an average pass completion rate of over 90 percent, per WhoScored.com.
Real would benefit from a player of his quality who can keep the ball well and dictate the game from the centre of the park. Currently, Madrid are heavily reliant upon Xabi Alonso for this role.
Any or all of Suarez, Ramires and Kroos would be fantastic signings for the Bernabeu outfit and could propel them to the La Liga title they missed out on in 2013-14.
Suarez and Ramires look unlikely considering the esteem they are held in at their own clubs, but large bids could potentially sway Liverpool and Chelsea.
Kroos, on the other hand, is looking to leave Bayern, and they may want to cash in on him before his contract runs out.