The 23-year-old has not featured as heavily as in recent campaigns for the Royals, making just nine third-tier starts in 2023-24 for the relegation-threatened club.
Holmes graduated from Reading's academy in December 2017 but had to wait until 2020 to really cement his spot in the first-team thinking, becoming a regular as the Berkshire club attempted to fight off relegation from the Championship last term.
The centre-back had a change of scenery for the 2019-20 term, when he has loaned out to Roeselare in Belgium's second tier, although he only made 11 appearances.
According to Football Insider, Luton are closing in on the signing of Holmes this month, with an announcement expected in the coming days.
The report claims that the youngster has arrived at the Hatters' training base and is currently undergoing his medical with the Premier League newcomers.
It is understood that Holmes will complete a permanent switch to Rob Edwards's side but will be immediately loaned back to Reading for the remainder of the campaign.
As well as Holmes, the Hatters are close to recruiting a second player from the cash-strapped Royals this month, in the form of fellow defender Nelson Abbey.
A product of the Berkshire club's academy, the 20-year-old has started 22 matches in League One for Reading this campaign, taking the role as captain in a couple of fixtures.
Royals head coach Ruben Selles has already confirmed that the club have agreed deals with top-flight Luton for both Holmes and Abbey.
The latter started alongside New Zealand teenager Tyler Bindon at the heart of Reading's defence for their clash with Port Vale on Saturday, although the contest was abandoned after 13 minutes due to a pitch invasion.
After throwing tennis balls onto the field of play in the third minute, hundreds of Royals supporters stormed the pitch in protest against majority owner Dai Yongge.
Selles's side sit 21st in the League One standings with 23 points from 25 games, meaning that they are three points away from safety as fans' frustration with the owners intensifies.
For the right to face either Crystal Palace or Everton in the next stage, Luton will do battle with third-tier side Bolton Wanderers at the Toughsheet Community Stadium on Tuesday night in a FA Cup third-round replay.