The English champions are understood to have come to terms on a £11million fee as they look to finalise a deal for the 21-year-old.
The former Barcelona Academy player will now discuss personal terms with the Premier League club.
City are short of left-back options following the departure of Oleksandr Zinchenko who left over the summer.
Joao Cancelo is currently the only senior specialist in the position, after City failed in their pursuit of Brighton defender Marc Cucurella.
Chelsea hijacked the deal after City failed to meet the £50million asking price, and the Blues quickly splashed £62million.
It is understood that City will continue their search for further options in the transfer market, with Gomez targeted as a development player.
He will be assessed in training and will have the opportunity to earn a place in the first-team squad but he could be sent out on loan to gain experience. Sister club Girona have been reported as a potential destination.
Gomez joined Borussia Dortmund after leaving Barcelona in 2018 and had a loan spell at Huesca before moving to Anderlecht, where he was managed by former City captain Vincent Kompany, last year.