The World Cup winner is believed to be keen on a move to Glasgow, amid rumours regarding his Dortmund future.
They claim that Celtic, or Liverpool, is the dream club for Grosskreutz should he leave this summer.
They also carry quotes from the player about his future. Speaking after returning to training after injury, Grosskreutz states:
"I'm simply overjoyed. During my time out, I even doubted myself if I would make it back.
"The next few weeks will show whether I will continue to play at Borussia Dortmund or not."
The 27-year-old has been at Dortmund for six years but last season only played 15 Bundesliga games because of injury and form.
But Grosskreutz is undoubtedly an excellent talent, as indicated by his place in the World Cup winning Germany squad in Brazil last summer, even if he did not make an appearance.
Originally a winger, he has adapted to become a multi-faceted player. Capable of playing in both full-back positions he would be welcomed with open arms at any club.
Could Celtic afford him?
The beauty of this deal is the fact his contract expires in 2016. Dortmund would not want to lose him on a free and after already plunging into their midfield this transfer market they would not be remiss to letting him walk relatively cheap.
Celtic have plenty of options in the full-back and wide positions but none with a World Cup winner’s medal. Considering his ability and standing a move from The Bhoys would be a dream for many a Celtic fan.
Injuries. Grosskreutz has suffered with thigh and hamstring injuries recently and underwent successful knee surgery in April. Considering the amount he would likely receive in wages per week Celtic will not want him on the treatment table. The last thing they want is another Derk Boerrigter.
But the fact remains he is a superb option, potentially available on the cheap and, apparently, is keen on a switch to Glasgow. He is definitely worth a roll of the dice.