The 20-year-old is looking for first-team exposure this season and, with his chances at Anfield appearing limited, he has been training with the Dutch outfit for the past week.
Tibor Pataky, co-owner of the CMG agency, revealed that there is also interest from the Championship, but hinted that playing in the Eredivisie would be more appealing.
"We have an old partnership with Groningen from a long time ago and the two clubs have been negotiating continuously," Pataky told Nemzeti Sport.
"Groningen have started pre-season with Krisztian, who has continued to train with them. We hope an agreement will be made this week. Anything can happen, but the plan is a loan contract.
"Krisztian is in a tough situation at Liverpool, but they don't want to sell him. We would like him to go to Holland. There is interest from the Championship, but he could use his creativity more in the Dutch championship."
Adorjan joined the Reds from MTK Hungaria in 2009.