The Blues made an enquiry for Madueke earlier this week and were told PSV had no interest in letting the 20-year-old leave, but that has not prevented Chelsea tabling a formal bid.
The England Under-21 international was formerly a youth team player at Tottenham and Chelsea head coach Graham Potter is said to have tracked him for some time.
“I know of the interest in Noni,” he said this week. “I’d rather not have that, but it’s not something I decide. The fact that there’s a lot of interest in him is of course due to his quality and his performances. But I do find it worrying. Because we’ve to see if we’re able to keep him, I hope so very much.
“We will certainly do everything we can [to keep him.] But you also know that things can change real quick if the interest heats up. As a club, you’ve got to be ready and have replacements lined up because if he leaves it would mean that we lose another player this winter.
“I’ve already indicated earlier what my wish was: that no player would leave in the winter break. That also applied to Gakpo and that applies to every player. As a coach, you just want to keep your best players, that’s clear. But there can also be situations like with Cody [Gakpo], where a certain type of club comes with a certain offer. Then it might be that it’s no longer possible to stop the deal from taking place. I hope that’s not going to be the scenario this time, but I can not exclude it.”
Chelsea are aiming to strengthen their attacking options this month and have already signed Joao Felix on loan from Atletico Madrid. They retain an interest in Shakhtar Donetsk winger Mykhailo Mudryk, but Arsenal are leading the race for his signature having made a third offer of over €70m to sign the 22-year-old on Thursday.