Both trophies come with the added bonus of European football if the winners finish the domestic league season outside the European places.
"It is true you need help from which team will win the League Cup or the FA Cup," the Dutchman told reporters.
"In that way we hope United will win at the weekend and one of the biggest clubs wins the FA Cup, because then it's possible seventh in the table can play a qualification for the Europa League."
Koeman believes Everton's involvement in Europe next season will be crucial to his plans for strengthening the squad in the off-season.
"Players like to be part of Europe and they like to be part of the Champions League," he added. "That is the best for football players but that will normally be impossible (for Everton).
"The first step is to be part of Europe even if that means being part of a difficult European league on a 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."
Koeman, whose team host basement-side Sunderland on Saturday, revealed that Everton had failed in their pursuit of several transfer targets before the start of the season because the club could not offer European football.
"Some players were interested last summer and... some wanted to see how we progressed (before signing)," he added.
"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 for next season."
Southampton are bidding for their first silverware since beating four-times League Cup winners United in the 1976 FA Cup final.
(Writing by Simon Jennings in Bengaluru; Editing by Clare Fallon)
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