The Hatters have signed six new players since getting promoted to the Premier League from the Championship at the end of last season.
Rob Edwards wants to bring in a new goalkeeper this summer as well and Manchester United’s Tom Heaton was his top target.
But with Erik ten Hag insisting on holding on to Heaton, Luton turned their attention towards Palmer and even have an agreement over a fee with West Brom.
But the move could fall through as Luton are struggling to agree on personal terms on a contract with the player.
There is a fundamental difference between the two parties over the inclusion of a relegation clause in the contract.
Palmer would see a significant rise in his wages if he joins the Premier League side, but it would drop off dramatically if Luton get relegated next season.
Luton are insisting on a relegation clause in the contracts of the players they are signing this summer, as they worry about the threat of the drop.
For the moment, a move for Palmer is stuttering as the player is not keen to have such a clause in the contract.