With 10 days remaining until the August 9 deadline, and the Owls looking to balance the books, speculation continues to link senior players like goalkeeper Keiren Westwood – a target for Stoke City – and striker Fernando Forestieri with potential exits.
Wednesday have already seen Jordan Rhodes and Jack Hunt join captain Glenn Loovens and Ross Wallace in departing Hillsborough this summer.
And with no new signings – coupled with unconfirmed reports the club are running under a transfer embargo for breaching Financial Fair Play rules – the last thing Owls manager Luhukay needs now is to see his squad suffer further cuts.
Asked if Wednesday could lose more players before the window closes next week, he replied: “We never know that. It is difficult to give an answer to that. In football every day is a new day.
“Maybe something can happen. The transfer window is always a problem when it runs later than the start of the season.
“This is pre-season and the transfer window is open until August 9, so you always have speculation.
“When the transfer window closes you can have 100 per cent focus and know what team you have.”
Before the window closes, Wednesday kick off their Championship campaign on Saturday at Wigan Athletic.
There has been no official statement from the club on the transfer embargo rumours – the English Football League have also refused to comment – while Luhukay told BBC Radio Sheffield “I don’t know” when asked about the club’s ability to bring in new recruits.
After spending millions on players like Rhodes, Forestieri, Joost van Aken, Adam Reach and Almen Abdi in recent seasons, the absence of summer signings speaks volumes.
Only last week QPR reached a £42m settlement figure with the EFL for breaching spending limits in 2013-14. Over the last 12 months Bournemouth and Leicester City have also been hit with fines for overspending.
Owls owner Dejphon Chansiri is determined to avoid similar punishment, meaning – self-imposed or sanctioned by the EFL – Wednesday’s financial outlay this summer has been limited.
It has left Luhukay to take the positives out of a pre-season that has seen him work with the same group of players with which he finished the previous campaign.
And with long-term injured van Aken and Steven Fletcher – who both played in Saturday’s friendly with Spanish side Villarreal – plus Kieran Lee and Gary Hooper all on the comeback trail, Luhukay certainly has options.
The Dutchman said: “We have five weeks of very good work behind us and we are happy with our preparation.
“We know the last two results in pre-season (defeats to Mansfield Town and Villarreal) were not positive, but that is not important as to whether we have a good start or not a good start.
“What matters now is having 100 per cent focus on Wigan this weekend and performing our best to win the points.”
One player likely to still be on the books at Hillsborough next month is striker Sam Winnall.
The former Barnsley forward spent the majority of last season on loan at Derby County until a cruciate knee ligament injury curtailed his campaign in February.
The 27-year-old’s fitness work is going well and Luhukay expects Winnall to return to training in a fortnight.
“He’s now two or three weeks back training,” said Luhukay. “He’s making progress, but he needs a couple of weeks before he can come back to the team training. He had surgery. Normally, this kind of injury takes six months. He is in this time period. He needs more time to come back 100 per cent.”
The Owls say they “vehemently refuted any form of racist abuse” over an allegation that Mansfield captain Krystian Pearce was abused in a pre-season friendly.
Last week’s match is already under investigation by the FA after both sides were involved in a mass brawl.