Bonucci, 30, has been heavily linked with a move away from Turin despite signing a new long-term contract until 2021 last year.
Chelsea and Manchester City are apparently interested in securing his signature as they both look to bolster their defensive ranks.
Antonio Conte wants to secure a reunion with him at Stamford Bridge after working with him during his time as manager of Italy and Juventus.
While Pep Guardiola is keen on bringing him to the club to help shore up his defence with John Stones struggling to live up to his £47.5million price tag.
But Spanish outlet Diario Madrista claim the Premier League duo will face competition from Real Madrid to sign Bonucci.
It is said the La Liga giants want to sign the Italy international as they bid to find a suitable replacement for Pepe.
The Portugal international will leave Real Madrid when his contract expires on July 1.
He has been linked with moves to Paris Saint-Germain and Besiktas in recent weeks.
Real have already recalled Jesus Vallejo from Eintracht Frankfurt to fill the void.
But Diario Madrista say the Spanish champions want to bring in an experienced defender like Bonucci to help solidify their defensive line.
However, securing a deal for him could prove to be difficult with his release clause set at £54m.
It is said that Chelsea are willing to pay this fee as Conte views strengthening his defence as a top priority.
But the chances of Bonucci leaving are apparently slim with the centre-back in favour of staying at Juve.
Speaking in March about a move to the Premier League, he said: “I’m owned by this club and the club will decide whether or not to sell me.
“I hope to honour the contract.”
