The Red Devils are said to have come to a "broad agreement" with Barcelona over the Netherlands international, with the midfielder set to move to Old Trafford.
However, a recent report claimed that De Jong wants to stay at his Catalan club this summer, and Koeman has also insisted that the 25-year-old is not looking for a move.
"The only thing I know is that Frenkie wants to continue at Barca," Koeman told Esport 3. "A couple of days ago he told me he wanted to continue. What I don't know is if Barca wants to sell him or needs money because he is one of the few players for whom they can get a good amount. For me, De Jong is a great player for Barca."
Meanwhile, according to L'Equipe, Marseille are prepared to listen to offers for Duje Caleta-Car this summer, with Wolverhampton Wanderers considering reigniting their interest.
Wolves are believed to have had a £13m offer for the defender turned down last summer, with Marseille unwilling to part with him ahead of the 2021-22 campaign.
However, the report claims that the French club are wary of losing Caleta-Car on a free transfer next year and therefore want to sell him during this summer's transfer window.
The 25-year-old was again an important player for his Ligue 1 side last term, making 38 appearances in all competitions, contributing two goals and one assist in the process.
According to 90min, meanwhile, Southampton are keen on signing Burnley midfielder Josh Brownhill during this summer's transfer window.
The 26-year-old was a key player for the Clarets during the 2021-22 campaign, making 38 appearances in all competitions, including 35 outings in the Premier League.
Burnley were relegated to the Championship at the end of last season, though, and there have been suggestions that Brownhill will be on the move in the current market.
Southampton have allegedly joined the likes of West Ham United, Everton, Leicester City, Wolverhampton Wanderers, Leeds United and Brentford in the race for his signature.
Over in Italy, Juventus are reportedly closing in on the signing of Angel Di Maria on a free transfer from Paris Saint-Germain.
The 34-year-old will officially leave his French club at the end of June, and there has been a host of speculation surrounding his future in recent weeks.
Barcelona were thought to be considering a move for the Argentina international, but Juventus have emerged as the favourites for his signature, and according to Sky Italia, the Old Lady are on the verge of bringing him to the club.
The report claims that the attacker will sign a deal worth almost £5m a year, and he is set to be joined in Turin by Paul Pogba, who is expected to return to the club after leaving Manchester United.
Di Maria was again an important player for PSG during the 2021-22 campaign, making 31 appearances in all competitions, contributing five goals and nine assists in the process.