The 29-year-old left-back found himself as second fiddle to the Ukranian Zinchenko this season, which has prompted him to seek an exit now.
The Cityzens have slapped a price tag of £15million for the English full-back and Leeds are looking to bring back their former player.
An academy graduate of Elland Road club, Delph played for around two seasons with the Whites before he became a mainstay at Aston Villa.
In fact, the England international spent an interim loan-spell with the Whites during his time at Villa Park.
Delph joined the Sky Blues in 2015 and couldn’t establish himself as a starter over the course. He has made a total of 89 appearances for the Cityzens.
The former Lions player has a contract until the end of next season.
Should Leeds move for Delph?
Marcelo Bielsa has a plethora of options to fill the left-back void back like Stuart Dallas, Ezgjan Alioski and Leif Davis.
And citing the price tag, the Whites should stick to their prime left-defenders rather than going all-out for Delph.
The Elland Road club missed great opportunity to secure a place in the Premier League next season.
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They will be playing Manchester United as a part of the pre-season campaign and Bielsa stated his desire to continue as the manager despite promotion slump.