The Brazilian has fallen out of favor with manager Erik ten Hag, who signed him more than a year ago.
While Ten Hag has publicly defended Antony, ESPN states that United are preparing to move him on in the summer.
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However, the finances of any deal would have to work, as Palace will demand a big fee for Olise.
The likes of Manchester City and Chelsea were interested in his services last summer.
Olise has experienced an injury ridden season with Palace in the Premier League.