The Dutchman swapped Southampton for Everton last year, but he will not be backing his former employers for Sunday's final at Wembley as a result of the potential implications for Everton.
"It is true you need help from which team will win the EFL Cup or the FA Cup," Koeman told reporters ahead of Saturday's Premier League game against Sunderland at Goodison Park.
"In that way we hope United will win at the weekend and one of biggest clubs wins the FA Cup, because then it's possible seventh in the table can play for qualification for the Europa League."
Koeman confirmed Everton qualifying for Europe will have an impact on the players the club tries to sign at the end of the season.
"Yes, it is a factor because players like to be part of Europe, and like to be part of Champions League," said Koeman, who led Southampton to the Europa League play-offs. "That is the best for football players, but that will normally be impossible.
"The first step is to be part of Europe even if it being part of a difficult European league on Thursday or qualification really soon in the pre-season. We would like to do it and be part of it because Europe is the next step.
"Some players were interested, but ok, maybe also some like to see how we progressed in Everton for the future. You will always fight against big clubs with more reputation and with more Champions League competition. But I think we are in a good way to get what we want in the team and for next season."