Real Madrid have offered Chelsea £100m for goalkeeper Thibaut Courtois as well as midfielder Willian, according to sources in Spain.
Courtois - who has one year remaining on his contract at Chelsea - has made no secret of his wish to move back to the Spanish capital, where his children live.
And Willian - who gave a good account of himself at the World Cup this summer - appears to be fielding a number of offers from some of Europe's elite clubs.
The Brazilian could have moved to Barcelona but the Catalan club were put off by Chelsea's £70m asking price and decided to spend half that on Malcolm instead.
Reports in Italy also emerged that the Blues have accepted a £66m bid from Manchester United.
However, Real Madrid appear determined to hijack that move and the Daily Mail has claimed Chelsea are "seriously considering" the double swoop offer.
The west London club will only have until August 9 to find a new keeper if they accept the bid with Jack Butland the most likely candidate to replace the Belgian.
Chelsea would then have until the end of the month to tie-up a deal with Madrid to send Courtois to Spain because La Liga's window will remain open until August 31.
Meanwhile, the signing of Willian could free Gareth Bale up more on the pitch ahead of the 2018/19 season.
The European champions have been quiet in the transfer market so far this summer, with right-back Alvaro Odriozola being Los Blancos' only summer signing.
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