The Council’s Cabinet is set to agree to buy a strip of land (marked C on the plan) between Wilton Rise/Cleveland Street and Chancery Rise when it meets on Tuesday.
The Council bought sites A and B in 2011.
The Chancery Rise link will be the location for the Councils £10 million access bridge into the York Central site.
The bridge will pass close to some houses on Cleveland Street and may affect the nearby playground.
There has been surprisingly little discussion with local residents about the plan which could have major noise and pollution implications.
No planning permission for the bridge is in place.
The Council is also looking to sell on site A to Network Rail. The site will accommodate some rail functions relocated from the York central area.
The affected streets fall within the Holgate ward. They are represented by Cabinet members James Alexander and Sonja Crisp.