The West Yorkshire club have spent big money to reinforce what has been a problem position for them for the past few seasons.
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James Trafford joined from Man City for a reported club record fee of £40 million, with add-ons potentially taking it to £45 million.
According to The Athletic, Eintracht Frankfurt goalkeeper Zetterer, 31, has been given permission to travel to England to sign for Leeds.
Zetterer signed for the Bundesliga club last summer, making 22 league appearances and keeping six clean sheets.
He will play as back-up to undisputed number one Trafford.