According to the Daily Mail's Sami Mokbel, Los Blancos have "regularly watched" the Lilywhites star ad would be able to offer him a significant pay-rise—Alli currently earns £60,000 per week.
The 20-year-old is said to be content to stay with Tottenham but is also "highly ambitious" and so could be tempted to follow in the footsteps of former Spurs stars Gareth Bale and Luka Modric.
Alli enjoyed a breakout campaign at White Hart Lane last season, racking up an impressive 10 goals and 11 assists in all competitions. As WhoScored.com revealed, he was one of the most incisive young passers in European football alongside Real's own Marco Asensio, who was on loan at Espanyol:
This year, he thus far has four goals and assists apiece in all competitions and is on course for a similar tally of key passes, having created 25 chances in 15 Premier League games, per Squawka.
The midfielder is still developing, of course, though the Evening Standard's Tom Collomosse believes he has regressed in one area of his game:
Another concern for Spurs could be his growing reputation for diving, which the Times' Oliver Kay reflected on after he controversially won his side a penalty against Swansea City:
Simulation perhaps isn't quite as objectionable on the continent as it is in the Premier League, however, so it's unlikely to factor into Real's decision if they opt to pursue him in the future.
Alli has the potential to become a real star—if he does, it will become increasingly difficult for Spurs to fend off the likes of Madrid and PSG.
Meanwhile, according to German outlet Bild (h/t Mario de la Riva of AS), Los Blancos are reportedly considering Borussia Dortmund's Sokratis Papastathopoulos as a possible replacement for Pepe and have made enquiries into signing him.
Pepe's current deal at the Santiago Bernabeu expires in the summer, but the 33-year-old has yet to put pen to paper on an extension.
The reliable and resolute Sokratis would be an excellent candidate to replace the Portugal international at centre-back.
Bleacher Report UK's Lars Pollmann has been impressed with his consistency and leadership abilities this season:
His passing has also improved significantly under Thomas Tuchel—according to Squawka, he has averaged an 89 per cent passing accuracy in the Bundesliga since the beginning of last season, a dramatic improvement on the 79 per cent he recorded during the 2014-15 campaign.
As such, he's been able to produce performances such as this, per WhoScored.com:
The 28-year-old is an experienced campaigner enjoying his peak years—he'd be an excellent candidate for any side looking to add a quality centre-back option to their side.
Real are no exception, though having to compete with Sergio Ramos and Raphael Varane for game time could prove off-putting for the Dortmund stalwart.