Zaha departed Palace on a free transfer last year, making the move to Galatasaray, and he represented the Turkish giants on 43 occasions last term, scoring 10 goals and registering five assists in the process.
The 31-year-old has another two years left to run on his contract at Galatasaray, but he is being linked with a move away this summer, and according to The Telegraph, Palace are exploring a loan switch.
The report claims that his large salary could prove to be problematic for the Eagles, but the capital outfit are working to bring him back to Selhurst Park for the 2024-25 campaign.
Zaha has made 458 appearances for Palace in all competitions, scoring 90 goals and registering 62 assists in the process, including 68 goals and 28 assists in 291 Premier League games for the Eagles.
A number of other Premier League clubs are also thought to be keeping an eye on his situation.
Brentford 'agree deal' for Napoli's Cajuste
Meanwhile, according to the London Evening Standard, Brentford have agreed a deal to sign Napoli midfielder Jens Cajuste.
The 24-year-old has been heavily linked with the Bees in recent weeks, and it is understood that he will join Thomas Frank's side on loan with an obligation to buy next summer.
Cajuste arrived at his current side from Reims in 2023, and he represented the Italian club on 35 occasions in all competitions during the 2023-24 campaign.
The central midfielder has another four years left to run on his contract at Napoli, but he has allegedly been made available for transfer during the current window.
Brentford will round off their preparations for the new campaign against Wolfsburg on Friday, before beginning their 2024-25 Premier League season at home to Crystal Palace on August 18.
Hull, Middlesbrough 'both keen on Conway'
Elsewhere, Hull City and Middlesbrough are allegedly both interested in signing Bristol City centre-forward Tommy Conway during this summer's transfer window.
The 22-year-old came through the youth system at Bristol City, and he has represented his current side on 92 occasions, scoring 25 goals and registering six assists in the process.
There is currently speculation surrounding the Scotland international's future, though, and according to Football Insider, Hull and Boro are interested in a move for him.
The report claims that Rangers have also been in touch with Bristol City, but the Scottish giants are unable to afford his price tag, which is in excess of £5m.
Burnley are also thought to be keen, with Conway set to leave the Robins this summer after the breakdown of his relationship with senior figures at the Championship club.