The newspaper reports that Getafe want £22 million for the centre-back and have already rejected a £12.8m offer from Monaco.
Djene's contract does not expire until 2023, which gives power to the Spaniards.
Although it is claimed that Arsenal, Tottenham, Everton and Crystal Palace are keen to secure a cheaper deal on the basis of the player having turned 28 last month.
Bournemoutn are also listed as suitors while Southampton are claimed to have enquired about Djene already.
But a move to the capital with Arsenal, Tottenham or Palace, or to Everton, where he would be managed by the legendary boss Carlo Ancelotti, could hold greater appeal.
Of those, Arsenal, Tottenham and Everton are perhaps most in need of strengthening in Djene's position, with Crystal Palace having conceded at least seven fewer goals (24) than the trio.
Djene, who can also play on the right or left of a back four, has made La Liga's team of the season in each of his two full campaigns there.
Have something to tell us about this article?