Reports on Monday suggested Barca had agreed to pay an initial €25 million for Depay, who is out of contract at the end of the season.
However, sources close to Barca told ESPN on Tuesday that the club simply doesn't have the cash to make signings at the moment, with Lyon president Jean-Michel Aulas later tweeting that his Barca counterpart, Josep Maria Bartomeu, told him the same in a conversation on Sunday.
Koeman, who coached Depay previously in his role as the Netherlands national team boss, said players need to be sold before Barca can even think about bringing in new faces.
"We're working towards the new season and I think we will go into it with the same group of players that we have now for pre-season," the coach told Fox Sports Netherlands.
Depay, 26, has been singled out by Barca as a possible target but the club's financial position, which has worsened during the coronavirus pandemic, means they desperately need to sell players and reduce the wage bill.
Ivan Rakitic has moved to Sevilla FC for €1.5 million and Arturo Vidal will join Inter Milan for a similarly low fee this week. Luis Suarez will also be allowed to leave if he can find a new club but none of those three players, despite commanding big salaries, will bring in big transfer fees to fund a spending splurge.
Barca had hoped to sell Samuel Umtiti, Rafinha and Jean-Clair Todibo but have not yet found buyers. They have also been, at various points in the summer, open to bids for Nelson Semedo, Junior Firpo and Philippe Coutinho, although the latter is now poised to be given a second chance at Camp Nou under Koeman.
All of that was relayed to Aulas by Bartomeu in a private chat, which sources confirmed took place to ESPN. The Barca president wanted to reach out given the sheer number of reports on the club's potential interest in Memphis.
"The Barcelona president told me on Sunday that they are suffering a lot due to the coronavirus crisis and there's no possibility of them making an offer," Aulas wrote.
Another source at the Catalan club told ESPN that Depay is not a possibility in the short-term because "the club's priority, above all else, is reducing the wage bill."
Barca's wage bill is the largest in football, with over €507m budgeted for sporting salaries for last season, according to the club's most recent financial report.
However Lionel Messi -- the club's biggest wage earner -- will be staying at the club despite trying to engineer an exit this summer. He reluctantly backed down from engaging in a legal fight with the club but in an interview was critical of the president and the board.
"That all went over my head," Koeman added about the Messi situation. "That was a dispute between Messi and the club. I have spoken to Messi since then and we are back to normal and continue to work with each other."