The 23-year-old spent the 2022-23 term on loan in the Championship at Middlesbrough, helping Michael Carrick's rejuvenated Boro reach the second-tier playoffs.
Despite the Riverside Stadium club losing out to Coventry City over two legs in the semi-finals of the playoffs, Giles still enjoyed an impressive season on Teesside.
A tally of 11 assists in the Championship from the left-back could only be bested by Sunderland's Jack Clarke and the Sky Blues' Viktor Gyokeres, with the latter recently securing a move to Sporting Lisbon in Portugal.
Having graduated through the Wolves academy, the defender has been sent out on loan six times from Molineux to the lower leagues of English football, however he could be on the move permanently this summer.
According to Sky Sports News, Luton Town are in advanced talks with Wolves over a £5m deal for Giles, as the Premier League newcomers look to add enough quality to avoid an immediate return to the Championship.
It is understood that the left-back is not part of Julen Lopetegui's plans in the Black Country for the 2023-24 campaign, meaning that the club are willing to offload him in this window.
The Spaniard signalled his intentions surrounding Giles early on in pre-season, leaving the defender out of his first-team squad which have travelled to Portugal to face Vitoria de Guimaraes and Porto.
A separate report from the Daily Mail claims that Wolves are looking to recruit veteran full-back Aaron Cresswell from West Ham United, in a deal which would supposedly cost £2.5m.
The 33-year-old only started 24 Premier League matches for the Hammers last season - his lowest number since the 2018-19 campaign - and it is believed that David Moyes is keen to sign a younger player in that area of the pitch.
The Hatters have mainly targeted young talent from the EFL this summer so far, bringing in Tahith Chong, Mads Andersen and Chiedozie Ogbene from Birmingham City, Barnsley and Rotherham United respectively.
Manager Rob Edwards has spoke candidly about how his side need to be effective on transitions in the English top flight this season, and a creative force from full-back such as Giles could help massively in that quest.
The Kenilworth Road club secured the signature of Manchester City youngster Issa Kabore on a temporary deal last week, with the 22-year-old joining the recently-promoted Hatters following a successful loan spell at Marseille in Ligue 1 in 2022-23.
Luton continue their pre-season preparations at Portman Road in East Anglia on Tuesday night, as Edwards's charges face an Ipswich Town side that scored 101 goals in League One last term.