The Clarets are preparing for their return to the Championship following a long stint in England’s top-flight, with Vincent Kompany at the helm at Turf Moor.
The report states that the recently relegated club are viewing Wallace as a potential Dwight McNeil or Maxwel Cornet replacement, as interest accumulates in the Burnley pair.
Burnley will have to battle it out with West Brom for the playmaker’s signature, with the Baggies holding a long-term interest, whilst Millwall are eager to strike a fresh agreement.
Quiz: Can you name which club these 27 ex-Burnley players are playing for now?
The 28-year-old netted six times and provided a further 11 assists for the Lions in the Championship last season, playing a major role in Millwall challenging for a play-off spot.
Wallace would be an excellent signing for any club in the Championship, and should the Clarets lose out on both Cornet and McNeil, then the 28-year-old would be an excellent, yet cost-effective option to bring in.
Possessing a high level of intelligence and a general understanding of the game that is unrivalled, Wallace’s technical ability, link-up play and relentlessness are also stand-out features of his game.
Given the interest currently in him, and the interest that is likely to continue to accumulate as this transfer window progresses, it will certainly not be an easy transfer for Burnley to complete.
A player who could quite easily be playing his football in the higher division next season, his immediate future continues to take centre stage.