The Daily Mail reports that the Ivory Coast striker, who has already confirmed that he is quitting Chelsea this summer, is in talks with former boss Jose Mourinho about a two-year deal to take him to the Bernabeu.
Drogba had been widely tipped to link up with former team-mate Nicolas Anelka in a big-money move to China, but internal strife at Shanghai Shenhua (which looks likely to see Anelka fired) and Mourinho's recent empowerment over transfers at Real means the 34-year-old Drogba looks set to move to the Spanish champions.
Fernando Torres, by contrast, will be sticking around at Stamford Bridge according to a report in the Independent after Roman Abramovich interceded to persuade the unsettled striker to remain at the Blues.
The back pages are full of the news that Lille's attacking midfielder Eden Hazard has decided to move to Chelsea rather than either Manchester City or Manchester United.
The Sun wins the battle of the headlines - at least for readers over the age of 30 - with its "Mancety Blank" headline, referring to a long-defunct gameshow hosted by Terry Wogan. The Daily Mirror is one of several papers to use an "Eden Project" headline, but it's their sub-head above chief football writer Martin Lipton's piece that caught our eye, both asking and answering its own question in one overblown swoop: "A swaggering prima donna at the age of 21... just why did Chelsea go so far to land the Belgium winger they are calling the heir to Messi and Ronaldo?"
Of the players heading out of Chelsea, on the other hand, Salomon Kalou is to sign for Schalke (according to the Daily Mirror) while Branislav Ivanovic is now being targeted by Barcelona as well as Real Madrid, the Daily Mail reports.
Barcelona's interest in Ivanovic comes as news emerges in the Daily Star that Vincent Kompany has rejected the chance to move to the Catalan club, the Manchester City captain instead pledging his long-term future to City.
Roberto Martinez will reject the chance to manage Liverpool, according to The Sun.
The Wigan manager will hold a press conference on Tuesday to reveal whether he will take Liverpool up on their offer to become first team coach - probably under the wing of former Bayern Munich boss Louis van Gaal - but The Sun reports that Martinez has made up his mind to stay at the DW Stadium.
Martinez's decision was apparently made on the back of promises from Wigan chief Dave Whelan to spend millions in the transfer market over the summer. With Martinez out of the equation, The Sun claims that Swansea's Brendan Rodgers or Borussia Dortmund'sJurgen Klopp will take the reins at Anfield.
Robin van Persie's future remains unclear as rumours of a move to Manchester City continue to circulate, but there is good news for Arsenal fans in The Sun: the player's mum has told him to stay put for the touchingly conservative reason that "they have no debts". Van Persie's wife, Bouchra, is also keen to stay, saying ,"our home life and our children are happy in London."
In other transfer news Manchester United are to make a £3m bid for Crewe's teenage play-off hero Nick Powell (Daily Star), Southampton are on the verge of signing Burnley's England U21 striker Jay Rodriguez for £6.5m (Daily Mirror), Blackburn's Yakubu is tipped to make a £1m move to Reading, Southampton or West Ham (Daily Mail), Jonathan Woodgate will get a new deal to stay at Stoke (Daily Mirror), Swansea are eyeing Tottenham's Mexican forward Giovani DosSantos (Daily Mail) and Reading have made a £2m bid for Nottingham Forest defender Chris Gunter (Daily Mail).