The Scottish giants have confirmed that the Reds have made an enquiry about signing the 18-year-old.
The youngster was expected to sign a new contract with Rangers this week.
Chief executive Martin Bain told the club’s official website: “Danny has been exceptional for us and where I’m at with those negotiations is that we have made him an offer – we’ve had many discussions – and there is a schedule that sits with his agent at the moment.
“Two English Premiership clubs approached us in January and since then I have had the odd discussion and we have seen people coming along to watch our players and you can see who they are coming along to watch.
“I can confirm that Liverpool have expressed an interest but a lot of clubs are keeping abreast of Danny’s situation.
“Danny is a young boy and has done exceptionally well, but I’m sure Walter would say he has a lot to learn and I would like to see him commit himself to Rangers and go on to become the Rangers player he can be.
“Sometimes in life you have to play the long ball and I hope this comes to fruition.”
