Mundo Deportivo says Diego Simeone's outfit will attempt to sign Giroud as a replacement for the released Diego Costa once the window re-opens next month.
The 33-year-old Frenchman has struggled during his near three years with the Blues to establish himself as first-choice.
Giroud, who has eight goals in his last eight matches for Chelsea, will become a free agent at the end of the season.
Lampard will be desperate to keep hold of him until the summer to help with his domestic and European aspirations.
But Atletico are allegedly hoping that they can persuade the West London side into business with a small cash offer.