Palace Sporting Director Matt Hobbs was Chief Scout at Wolves when they signed the 28-year-old and had become Sporting Director when they sold him to West Ham in 2024.
Palace are not currently expected to progress a move for Kilman, but are struggling in their search for a centre-back.
Kilman is currently out of favour at West Ham, having been benched for their last four matches. However, he has still made 23 appearances for the Premier League strugglers this season.
A loan move for Josh Acheampong has been rebuffed by Chelsea, while an attempt to sign Jhon Lucumí from Bologna was unsuccessful.
Palace also made a bid for Club Brugge defender Joel Ordóñez in recent days, which was turned down.
The Selhurst Park club have yet to replace FA Cup-winning captain Marc Guehi, who joined Manchester City for £20million two weeks ago.
They face a race to this evening’s 7pm transfer deadline to add an option at centre-back, or will have to rely on Jaydee Canvot and Chadi Riad as their options to play on the left of the back three.
Midfielder Jefferson Lerma has also provided cover at centre-back, though has been required in midfield in recent weeks due to injury and suspension.