Costa has been away from Leeds at Valencia and Al Ittihad on loan over the last two seasons, but returned to the club earlier this summer.
It was thought the winger could be involved as Leeds begin their Championship campaign, but he was not in the mix for the loss at Birmingham City on Saturday.
And the winger looks like being on his way out, with Farke confirming that Costa is keen to leave Elland Road this summer.
The German manager told his press-conference after the Birmingham game: “Quite open with Helder he wants to leave the club.”
Farke is willing to now trust those above him at Leeds to bring in the reinforcements needed in what remains of the summer transfer window.
“There’s confidence. I totally believe in the quality of our people”, he said.
“Sometimes it’s a bit difficult. We can’t make ourselves a different reality. But it’s about staying calm, not to panic.”
Leeds did make a signing within the last few days, with defender Joe Rodon arriving at the club on loan from Tottenham Hotspur.