Both sides are looking to strengthen their options before the transfer window closes on 1st September.
Palmer is a player they are interested in, but Manchester City appear to have yet to make a firm call over what to do with the youth product.
Brighton and West Ham are waiting to see what Manchester City want to do and both would be prepared to try to sign him permanently if he becomes available.
If Manchester City do agree to sell the midfielder, they would want a buy-back clause including in any deal to give them continued control over his future.
The 21-year-old was handed a ten-minute outing in Manchester City’s Premier League opener against Burnley.
Palmer also featured in the Community Shield curtain-raiser against Arsenal.
In total the midfielder has turned out for Manchester City’s first team on 40 occasions, but may find securing regular game time a bridge too far at the Etihad.
