Sources have told ESPN that United are exploring a loan deal for Dembele, who was on the bench for Barca's 4-0 win over Villarreal on Sunday, with little progress being made in their move for Jadon Sancho.
However, sources at the Catalan club have told ESPN there has been no contact with United since they initially sounded out the possibility of signing the France international earlier this summer.
"This is a situation to be resolved by the club and the player," Koeman told a news conference on Wednesday ahead of the league game against Celta Vigo,
"As long as the player is with us, he is part of my plans. He didn't start [against Villarreal] because there are other players, too, and Ansu Fati has demonstrated that he is good enough to play.
"Ousmane has to wait for his chance. He was better physically in the first few weeks of preseason. He has dipped a little bit in the last week, but he trained well today and I'm counting on him."
Dembele, 23, joined Barca from Borussia Dortmund for an initial fee of €105 million in 2017. His time at Camp Nou has been blighted by injuries, though, and sources close to the club have told ESPN that any "serious" offers would be entertained.
Moving Dembele on would allow Barca to turn to the transfer market themselves, with Koeman admitting he still wants to sign a centre-back and a striker. Manchester City's Eric Garcia and Lyon's Memphis Depay are targets, according to ESPN sources.
"We know the club have financial limitations but there are two or three positions we're working on," Koeman added.
"There's nothing certain at the moment. We're a little weak in the centre-back position for the season that lies ahead of us, while we're also looking for another No.9."
Barca are set to sign is Ajax's Sergino Dest as Koeman confirmed the right-back has undergone a medical at the club. He previously tried to convince the defender to represent Netherlands before Dest decided to pledge his future to the United States.
"Dest will be a very useful player for Barca," Koeman said. "I spoke to Sergino before about the national team because he had the chance to play for Holland or the USA. But the decision must made be by the player, [based on] his feelings from inside and what prefers.
"And I think it's good for American football that they have players like Dest, like Konrad [de la Fuente] here in Barcelona."
The start of the La Liga season has allowed a little bit of calm to return to Barca following a turbulent summer in which Lionel Messi tried to leave the club.
Messi has since apologised to Barca supporters and said he was acting in the best interests of the club and called for everyone to pull together in the pursuit of success this season.
"I don't know I will have a quiet life as Barca coach after Messi's comments, but I don't think so -- there's always something." Koeman joked when asked if the end of the Messi saga would help restore focus around the club.
"But, of course, it's very positive that the club captain calls for us to be united and I hope we're going to be a little calmer than have been recently."