The 27-year-old was a standout performer for the Tractor Boys last season as they secured promotion to the Championship, finishing second in League One behind champions Plymouth Argyle.
Walton was an ever-present for Ipswich in the third tier and kept a division-high total of 22 clean sheets, helping Kieran McKenna's side to concede just 35 goals in 46 league matches.
The former Wigan Athletic man has played his senior football exclusively in the Football League, however he could now be handed the opportunity to test his credentials in the top flight of England.
According to journalist Alan Nixon, Luton have added Walton to their shortlist of potential arrivals in the goalkeeping department ahead of the 2023-24 campaign.
The Hatters are having to broaden their search for a new first-choice stopper, with a number of their targets turning down moves to Kenilworth Road this summer.
It is understood that 37-year-old Tom Heaton was admired by Luton and would have been welcomed to Edwards's squad, however the former Burnley man is reportedly set to stay at Manchester United next season.
The Red Devils were supposedly 'reluctant to let him leave' to Kenilworth Road or elsewhere in this transfer window, despite the arrival of Andre Onana from Inter Milan in response to David De Gea's exit from Old Trafford after 12 years.
Luton are also said to have failed in an attempt to secure the services of West Bromwich Albion stopper Alex Palmer over the weekend, with the Baggies rejecting an up-front offer for the player.
Reports circulated that the 26-year-old's move to the Premier League was close to being confirmed after he was left out of Carlos Corberan's squad which travelled to Bolton Wanderers on Saturday afternoon, however it is understood that the Championship club have turned down a bid in excess of £3m.
Attention for Luton now moves to the capture of Ipswich's Walton, however it is believed that the keeper is currently settled at Portman Road and is looking forward to playing Championship football in East Anglia.
James Shea and Matt Macey are the only goalkeeping options for Edwards as the Hatters' pre-season schedule reaches its conclusion, with the duo managing just one league appearance between them in the 2022-23 term.
Luton have targeted talent from the Football League so far this summer, recruiting the likes of Chiedozie Ogbene and Tahith Chong from Rotherham United and Birmingham City respectively.
Ryan Giles has also arrived at Kenilworth Road from Wolverhampton Wanderers after impressing during a loan spell at Middlesbrough in the Championship last season, with Edwards looking to build a team which is capable of being deadly on transitions in the top flight.
A trip to Europa League-bound Brighton & Hove Albion awaits the Hatters on August 12, meaning they have less than a fortnight to bring in a new first-choice goalkeeper.