James Rodriguez has told Real Madrid he wants his future resolved soon, Sky sources understand.
The Colombia midfielder, who has had a lack of first-team opportunities at the Champions League winners, has been told he can leave the club for £62m.
His agent is believed to have offered him to Chelsea, Liverpool, PSG, Inter Milan and Juventus.
Rodriguez, who was left out of Real's squad for the Champions League final win over Juve last month, has also been linked with a switch to Manchester United.
His team-mate Luka Modric has warned him that leaving the club to join Jose Mourinho's side would be a mistake.
Modric, who joined the Spanish champions from Tottenham in 2012, told newspaper Marca: "It's certainly not an easy decision to leave Madrid.
"When you leave here, nothing is the same. You're at the best club in the world, that's for sure, and from there you can only go down.
"Everyone will have their reasons. If I continue like this, I will do everything possible to stay, but things in football change fast."
Rodriguez joined Real in 2014 for around £71m from Monaco after being named the Golden Boot winner at the last World Cup.
Zinedine Zidane's side start their pre-season fixtures against United on July 23 in California.