The 21-year-old winger has faced criticism in recent weeks after failing to find consistent form for the Red Devils since his big-money transfer to Old Trafford from PSV Eindhoven in the summer.
Depay has scored just one Premier League goal for the Red Devils and was left out as United beat Everton 3-0 in the top flight last weekend.
However, Southampton boss Koeman feels that the attacker needs to be given time to adapt to the rigours of the English top flight and is backing Depay to come good at Old Trafford.
He also revealed that the Saints were monitoring the winger before his eventual switch to United.
Koeman is quoted as saying by Metro: “I think Depay, now at the moment, has a difficult time but that’s normal because he’s 21 and of course maybe the step to Manchester United in all respects is a difficult one and he needs more time.
“If one day he will be on the market, I’m interested yes but I don’t think so because I believe in him.
“It’s a difficult time but [he is] still young. He has to improve a lot and he will go through all these difficult moments.
“It is true, we were interested in Depay last year but we heard from his management that he wanted to stay one more year in Holland and then take the opportunity to play for a foreign club.”
United take on CSKA Moscow in the Champions League on Wednesday night.
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