McDermott has signed three players during the summer, but had suggested he would have to sell in order to add anymore new faces to his squad.
The former Reading boss revealed after the weekend defeat to Nuremburg however, that there had been some interest in one of his current players and this could lead to one more new arrival ahead of Saturday's opening league fixture against Brighton.
"We've had a little bit of an enquiry," McDermott said. "Monday, Tuesday we'll see what happens.
"Maybe that would let me do something the other way.
"If someone left the building, someone could possibly come in. That's how it is."
Leeds closed their pre-season fixture programme with a 4-0 win over Irish side Shelbourne on Monday evening.
Winger Ryan Hall scored twice, while Noel Hunt and Ross Killock were also on the scoresheet.
McDermott told the club's official website: "I was delighted with the whole group.
"We got up at 4am, travelled out here, played at night, and did very well.
"It shows the attitude of the group. They applied themselves well and were professional.
"I was very happy, it was a good mix we had with us."