The Hatters are back in the top flight of English football for the first time since the Premier League was created, with Rob Edwards looking to ensure his side can avoid an immediate return to the Football League.
The Kenilworth Road club fought off promotion pushes from the likes of Palmer's West Brom to secure a top-six finish in the Championship, and Luton subsequently went on to beat Coventry City in the playoff final at Wembley to book their place alongside England's elite.
Albion's first-choice goalkeeper featured 23 times in the second tier last season, keeping 10 clean sheets and helping the Baggies to an externally respectable - yet internally disappointing - ninth-placed finish.
According to the Express & Star, a deal which would have seen Palmer transfer from West Brom to Luton is now off, with the stopper set to appear in the Championship again next term.
It is understood that the Hatters submitted a formal bid to the Black Country club for the 26-year-old over the weekend, and that offer had immediate consequences on the pitch.
Palmer was left out of Albion's squad which travelled to Bolton Wanderers on Saturday afternoon, with second-choice keeper Josh Griffiths playing the full 90 minutes as the Baggies lost 4-3 in their final pre-season friendly of the summer.
The report claims that Luton were willing to pay the transfer fee for the Englishman up-front rather than in instalments, meaning Carlos Corberan's men were initially open to considering the deal.
Although the Hatters had supposedly made a bid in the region of £2.5m-£3m, it is now believed that the true offer was higher, although it was not significant enough to lure West Brom into a sale.
Luton's search for a new goalkeeper looks set to continue into August, with the Premier League newcomers having less than a fortnight before their season opener at Brighton & Hove Albion.
Nottingham Forest's Ethan Horvath arrived at Kenilworth Road last summer on a loan deal, and the American kept an impressive 19 clean sheets as Edwards's charges earned promotion to the top flight.
James Shea and Matt Macey are the only players currently in the goalkeeping department at Luton, meaning the club's recruitment team will be working frantically over the next month to provide the Hatters with a genuine first-choice option between the sticks.
West Brom have snubbed a respectable offer for Palmer and will hope the 26-year-old can help them challenge for the top six once again this season - although the club's finances are restricting their dealings in the transfer window.
The Baggies are no longer receiving parachute payments from the Premier League and will have to rely on the free transfer and loan markets this summer to improve their squad.