If a deal is completed, the forward will be handed another chance of impress in the Championship.
The Tykes endured a miserable 2021/22 campaign as they were relegated to League One.
Luton meanwhile reached the play-offs last month where they suffered a 2-1 aggregate defeat to Huddersfield Town in the semi-finals.
Since joining Barnsley on a permanent deal from Fulham in 2019, Woodrow has gone on to feature regularly for the club.
With Woodrow’s deal at Barnsley set to run until 2023, this summer window represents a chance for the club to secure a reasonable fee for his services.
Luton will be keen to bolster their attacking options this summer as they look to launch another push for a top-six finish in the Championship next season.
The Hatters will be able to call upon the services of strikers Elijah Adebayo, Harry Cornick and Cameron Jerome later this year whilst discussions are ongoing with Danny Hylton over his future.
Quiz: Can you name which club Luton Town sold these 16 players to from the last decade?
Providing that Luton are able to reach a breakthrough in negotiations with Woodrow, this could turn out to be a clever bit of business by the club.
A product of the Hatters’ youth academy, Woodrow left the club in 2011 as he sealed a switch to Premier League outfit Fulham.
During his career to date, the forward has demonstrated that he is more than capable of competing in the second-tier.
When you consider that Woodrow has scored 44 goals in the Championship, it wouldn’t be at all surprising if he hits the ground running at Kenilworth Road next season as he will unquestionably be confident in his ability to deliver the goods.