The midfielder's current deal at the City Ground is due to expire at the end of this campaign, which if no agreement is reached, would see him become a free agent.
Despite having expressed his desire to retain the 24-year-old's services, Davies was also quick to insist that his team would cope should McGugan opt to leave.
"I have spoken to Lewis McGugan. He has scored five goals for us now. He showed tremendous courage with the penalty and he knows my feelings about him," said Davies. "We will remain focused on the remaining games, then we will sort out the things that need sorting in the future. I don't worry about losing players. They come and go.
"We make our intentions clear to players. When we want them to stay, we will offer them what we can, financially speaking. If they decide to move on to pastures new, I do not lose too much sleep about it. There are far too many players out there to worry about that.
"He knows my feelings, he knows my position and he knows how much he is wanted at this club."
McGugan has spent his entire professional career with the Tricky Trees.