The 21-year-old winger, who was part of the Boro side beaten 4-1 at Bristol City on Sunday which left them second from bottom, has already been the subject of interest from Championship clubs.
Chairman Phil Wallace told the club website: "Luke has been brilliant for us, but we are under water financially and if the right offer comes in for him and for us, we shall have to consider rebuilding without him.
"Due to the carry-over of contracts from last season, our budget is the highest in our history and a good part of the overspend is invested in players that Graham Westley would choose not to have, given a choice.
"That would be manageable if our gates were rising, but we are six figures down on gate income over last season at the halfway mark so it's hurting.
"But we're an optimistic lot at Stevenage and it would be a brave man that bets against us not enjoying a strong second half to the season."