Boss Stephen Robinson confirmed Motherwell are looking into allegations about striker Jacob Blyth's behaviour on holiday.
The 24-year-old striker joined the Steelmen last summer from Leicester but made only one start last season.
Earlier in the month he was ruled out of action for four to six months after an operation to repair a foot injury.
Blyth was photographed this week in Marbella, Spain, apparently inhaling from a balloon and the Fir Park club are now looking into it.
Ahead of the home Betfred Cup game against Morton on Saturday Robinson was asked about the newspaper report.
He said: "We are obviously well aware of it. It was on the back page of the newspaper. It is being dealt with internally.
"That's the most we need to say at this stage.
"We are looking into it and it will be dealt with appropriately."
Following a 5-1 win over Queen's Park in the opening Group F match at Hampden Park last week, Robinson is expecting the most difficult test of the section against Morton.
He said: "Jim Duffy's team will be well organised. Make no mistake we are in for a tough time.
"It is still very much pre-season, people are still finding their feet, they are finding an understanding of each other.
"Bearing in mind we brought nine new players in, it is going to take a little bit of time but we are pleased to get off to a winning start."
New signing Andy Rose, who arrived from Coventry on an initial one-year deal, made his debut as a second-half substitute against the Spiders.
The 27-year-old Australian midfielder was suitably impressed by the Hampden Park playing surface but is expecting Fir Park to be of a similar standard.
He said: "I am expecting our ground to be the same for sure.
"I have already spoken to the groundsman a few times, he is a great guy and obviously has done an incredible job with our pitch.
"For all of us new boys, that is the most exciting part of this whole thing - to get going at Fir Park in front of our fans, we have heard great things about our pitch and the way it is cared for.
"They are not all going to be at Hampden or Fir Park but I can't wait to get going here."
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