The 24-year-old is currently in his second season on loan at German club Hertha, where he is an important player.
Despite Grujic’s good form, breaking through at Anfield is proving difficult, so he is being offered to clubs.
Milan, who are being linked with many Bundesliga players ahead of Ralf Rangnick’s arrival, are one of them.
However, TMW states that the Rossoneri are cold on the idea and may have other priorities.
Lazio do have an interest in Grujic and could look to take him on loan from Liverpool.
The Serbian international joined Liverpool from Red Star Belgrade in 2016 for £5.1m, but has mainly been loaned out.