Grujic was the first signing of the Jurgen Klopp era, joining from Red Star Belgrade in January 2015 and remaining there on loan for the rest of the season.
The 20-year-old Serbian has been dogged by injury in his maiden campaign at Liverpool and has made just five appearances in all competitions.
His lack of football has not dampened the interest of Dinamo, however, who would be interested in securing his services on a temporary deal.
"I wanted to bring Andrija Zivkovic in from Benfica for €5million, but I failed," Dinamo adviser Zdravko Mamic told Serbian publication Blic.
"Now I want to get Marko Grujic from Liverpool on loan."
The news may pique the interest of Liverpool, who have been persistently linked with Dinamo youngster Ante Coric.