The newspaper says the 21-year-old is valued at around £35m and Spurs see Chillwell as a long-term replacement for Danny Rose but Leicester City are expected to do all they can to hang on to the left-back.
The Reds midfielder has witnessed De Jong's ability at close range in the Holland squad this week.
De Jong, who made his senior global debut for Holland earlier this month, played the full 90 minutes as they lost to France in the UEFA Nations League on Sunday evening.More news: Russians rally against raising pension age
Reports also claim that Tottenham made a bigger offer for De Jong, though those overtures were also rejected.
"Barcelona may return for Frenkie in January but it's unlikely that players will leave in that period". The Catalans can't afford to let him slip out of their grasp due to him being the ideal heir for Sergio Busquets, and even more importantly they can't afford to let Real sign him because they already have one of the strongest midfield in world football. So, Overmars has made it clear that De Jong will not be allowed to join Barcelona in the middle of the season. I'm staying at Ajax.
"Frenkie is a great player, he did a good job", Wijnaldum said. The club technical secretary Eric Abidal held regular conversations with the player's representatives over the past few months, while also negotiating with Ajax director Marc Overmars.
De Jong moved to Ajax from Willem II in 2015, and represented Jong Ajax before stepping into the first team.