According to new legal docs, obtained by TMZ, Gap wants Kanye to foot the bill for any damages it might incur in a lawsuit it's facing ... because Gap feels Ye and his company are responsible for putting them in this mess.

As for that mess -- Gap is being sued by Art City Center, a company that says it owns a building in downtown L.A. that was leased to Gap as a storefront for Kanye's Yeezy clothing line.

Art City Center says the building underwent a ton of unapproved alterations when Gap was hawking the Yeezy collab in 2021 and 2022 ... and the company is suing Gap over the cost to restore the premises. So, Gap is, essentially, trying to pass that buck to Kanye.

In the suit, Gap says its contract with Kanye called for Gap to not be held liable for any claims like this that might be brought against them.

Gap is going after Kanye for more than $2 million ... which includes the amount the company thinks it's about to get dinged for over the Yeezy store -- plus a little extra for Gap's attorneys' fees, of course.

As we reported ... Kanye pulled the plug on his partnership with Gap back in September, claiming the company double-crossed him with empty promises.

We reached out to Kanye's camp ... so far no word back.