Koeman has a year left on his contract, but president Joan Laporta says they will meet next week to decide whether or not he will remain in his post.
What has been said?
While De Jong is in the dark about what will happen next, he says he has a special connection with Koeman and hopes he continues at Barca.
"A lot is being written now. I haven't had any contact with people from the club now, nor with Koeman, so I don't know what's going on. What I hear, you hear too. I'll wait," the midfielder told Nu.nl.
"I don't know if that's true [that Koeman will leave]. I can't judge that. All I can say is that I have a good relationship with Koeman. For me he is a good coach. So I hope he stays."
He added: "Barcelona is, of course, one of the biggest clubs in the world. If you don't become champions, there's always nagging. So in that sense it doesn't surprise me [that there is speculation]."
What is going on between Koeman and Barcelona?
The relationship between club and coach appeared to sour this week when Laporta said at a press conference that Koeman, who suffered a heart attack last year, recently ended up in hospital after an "episode".
The former Netherlands manager's agents expressed their frustration in a post on Twitter that was subsequently deleted.
Wasserman wrote: "Imagine: I want to marry you, but I have doubts. Give me two weeks to find a better partner. If I can’t find the right person, we will get married anyway!"
Koeman followed up with a Tweet of his own insisting he was fine, writing: "Don’t believe anything you hear. I am healthy, that’s all that matters in life!"
How did Koeman's first season at Barcelona go?
The 58-year-old took over at Barca last August, replacing Quique Setien at the helm.
They have played 54 matches under him and won 35, losing 11.
While they underperformed in the Spanish top-flight and Champions League, they won the Copa del Rey with a 4-0 win against Athletic Club in the final.