The paper says that Real boss Jose Mourinho has decided that their current right-back - former Liverpool defender Alvaro Arbeloa - is not up to the job and has identified Tottenham's Kyle Walker and Liverpool's Glen Johnson as potential replacements.
"Madrid have already set aside a £16.5m fund to sign one of the two, but are confident of netting a bargain once talks get under way," says the paper.
Walker, who was once dubbed the 'new Roberto Carlos' by the Spanish press after a superb performance for the England U21s against Spain, would be the more expensive option as he is still only 21.
His fellow England international Johnson could by cheaper as he is now 27 and coming off an injury-hampered season at Anfield, although he did also sign a contract extension in 2011.
"Scouts from Madrid have watched both players this season, and the club will decide which way to go at the end of the season," the Daily Star adds.
"Also on Real’s radar is Ajax defender Gregory van der Wiel, but sources in Spain feel he is more likely to join Chelsea."
Mourinho has attempted to play down the rumours, which first surfaced in Spanish sports daily Marca.
Elsewhere, and Dirk Kuyt's six year spell at Anfield could be about to come to an end according to the Sun.
The paper says that the Dutchman, along with Argentine winger Maxi Rodriguez, is likely to be the high-profile casualty of Liverpool’s summer rebuilding.
"Italian duo Roma and Fiorentina are on red alert, while Turkish outfit Galatasaray are another team monitoring him. Former club Feyenoord would also love to take him back if they are not priced out," reveals the paper.
Chelsea and Manchester United are leading the race to sign Japan forward Shinji Kagawa who is refusing to sign a contract at Borussia Dortmund. The German club have given him two weeks to decide on a contract extension to 2016 that would double his salary from £1.25mi per year to £2.5m. But they would be forced to sell Kagawa in the summer or risk losing him for nothing when his contract runs out in 2013. (Daily Mail)
Manchester United are also said to be chasing Spanish star Oscar de Marcos - the Athletic Bilbao flier who knocked them out of Europe. Highly-rated De Marcos will be watched by United’s chief scout Jim Lawlor after boss Sir Alex Ferguson’s brother Martin looked at him last week. (Daily Mirror)
Arsenal boss Arsene Wenger is considering lining up a shock move for Swansea's goal ace midfielder Gylfi Sigurdsson. The Icelandic international is only on loan at the Liberty Stadium from German side Hoffenheim.
Newcastle United boss Alan Pardew is ready to sign Barnsley midfield starlet Jacob Butterfield in a shock deal worth up to £2m. Butterfield, just 21, was skipper of the Championship side before he picked up a serious injury - and the Toon spotted his potential and have teed up the move despite his current ailment. (Daily Mirror)
Manchester City have beaten rivals United to the signing of Belgian starlet Mathias Bossaerts. The teenager has been on the radar of some of the top teams in Europe, including Liverpool. But the 15-year-old has agreed to join City in a four-year deal that will see him arrive in England at the end of the season. (Daily Mirror)
Stoke City are considering making a £6m summer swoop for Wolves winger Matt Jarvis. (Daily Star)
Burnley boss Eddie Howe has put Newcastle and Southampton on alert by conceding 21-goal striker Jay Rodriguez could be sold in the summer. Both clubs have made bids for Rodriguez, 22, in the recent past and still fancy a move for the prolific star. (Daily Mirror)
Future Heerenveen boss Marco van Basten is determined to put the block on striker Bas Dost's proposed £7m move to Aston Villa. (Daily Star)
Tottenham are still looking for a replacement for Harry Redknapp if he takes the England job and Antonio Conte, the Juventus coach, has emerged as a potential candidate according to the Daily Telegraph.
"The 42-year-old former Italy international midfielder, who ended his career at Juventus after making more than 400 appearances in the black-and-white shirt, is understood to be taking English lessons," says the paper.
Finally, Ole Gunnar Solskjaer is at the top of Wolves owner Steve Morgan’s shortlist to become the club’s new boss. The multi-millionaire has identified the former Manchester United striker along with ex-England skipper Paul Ince as the prime long-term candidates to succeed Mick McCarthy. (Daily Mail)