The 33-year-old, who was Sir Alex Ferguson's final signing for Manchester United back in January 2013, has been a free agent since his Galatasaray contract expired at the end of June and has posted footage on social media of himself working out at Palace's Beckenham training ground.
Born in Abidjan, the Ivory Coast international first came through Palace's academy before his move to United, and his second Selhurst Park spell, which began in 2015, established him as the club's all-time leading Premier League goalscorer.
Zaha scored 90 goals in 458 appearances across two spells with the Eagles, the second of which ended in 2023 when he left for Turkey on a free transfer, before later spending time on loan at Lyon and MLS side Charlotte.
His arrangement to use Crystal Palace's facilities is informal, according to The Sun, with the club having agreed to grant him personal access purely to help him stay fit while he searches for a new club.
A longer-term return is not currently under consideration, despite growing excitement among supporters and a comments section full of fans urging him to come back after he posted a training montage on Thursday.
Chairman Steve Parish is understood to be comfortable letting Zaha continue using the facilities given his history with the club, but the decision on any playing return rests with the football department rather than sentiment. Palace have already strengthened out wide this summer by signing winger Dwight McNeil, while also weighing up a move for Brighton's Solly March.
Zaha's brief United career yielded only four senior appearances before he returned to Palace, where he went on to become one of the club's most celebrated modern players. Should no suitable offer emerge elsewhere, his continued presence at Copers Cope means the option of a familiar training base, even without a club to play for, remains open to him for now.
Champions League clubs including Atletico Madrid were previously linked with his signature before his move to Turkey, a reminder of the level he once operated at before injuries and inconsistent form disrupted his career in his thirties.