The 23-year-old is now back training with the Baggies having spent the 2019/20 campaign on loan at Plymouth Argyle.
Palmer played an integral role in the Pilgrims winning promotion from League Two, with manager Ryan Lowe hailing him the best keeper in the division.
But his current Albion contract is set to expire at the end of this month.
Talks over a new deal have been positive, however, with the Express & Star understanding the Baggies will soon announce Palmer has agreed a new three-year contract.
Speaking last week, Lowe confirmed he would be keen to re-sign Palmer.
But he said he believes the keeper is good enough to secure a loan move to the Championship, while he also felt Palmer may want to stay with the Baggies and fight for a place in the match day squad.
Palmer’s loan to Plymouth was due to cover the entire 2019/20 campaign.
That means he is not available to head coach Slaven Bilic for Albion’s remaining nine Championship matches.
He will only be able to feature this term if the Baggies receive emergency dispensation following an injury crisis.
Originally from Kidderminster, Palmer has previously had two loans with hometown side Kidderminster Harriers.
Prior to his temporary switch to Plymouth, he also had two seven-day emergency loan spells with Oldham and Notts County.