The 20-year-old midfielder is held in high regard at Anfield but currently sees his path to the first team blocked by experienced international performers.
Liverpool are keen for him to get games and have allowed the youngster to spend the past week in Holland.
Discussions regarding a short-term deal are being held and the agency which looks after Adorjan are confident an agreement which suits all parties will be reached.
Tibor Pataky, co-owner of the CMG agency, told Nemzeti Sport: "We have an old partnership with Groningen from a long time ago and the two clubs have been negotiating continuously.
"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."
He added: "They recognise that a 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."