The 22-year-old life-long Dortmund fan broke into the Germany squad this season on the back of impressive form which has helped steer Dortmund towards
their first German league title since 2002.
With his side currently seven points clear at the top of the table with six games left to go, Borussia are edging ever closer to the Bundesliga shield and a Champions League place next season.
But Grosskreutz, who scored as Dortmund came from behind to beat title rivals Hanover 4-1 at home last Saturday, is refusing to get a haircut until his team are crowned German champions.
"We are slowly getting towards the title and then I can get my haircut," he admitted. "I have never had it so long before, I bet last October that I wouldn't get it cut until we win the league."
Hamburg coach Michael Oenning has said he hopes Dortmund win the title, but plans on pulling off an upset when they host the German leaders.
"I like Dortmund and would be happy if they are champion," said the 45-year-old, who took over after Armin Veh was sacked last month. "But we will cook something up for them."
And Hamburg captain Heiko Westermann, who used to play for Dortmund's rivals Schalke, said he wanted to beat the leaders to open up the title race.
"We want to reward our hard work by beating Dortmund to make the league exciting again," said the Germany defender.
Hamburg are seventh in the table and four points off a place in the Champions League.
"We need the points not only for our confidence, but also to achieve our goals," said Oenning.
Second-placed Bayer Leverkusen can expect few problems on Sunday as they host St Pauli, who are waiting to hear their punishment after last week's game with Schalke was abandoned after the assistant referee was hit by a beer cup.
Defending champions Bayern Munich are up to third in the table and are at Nuremberg in the Bavarian derby on Saturday.
They have few injury problems and only defender Daniel van Buyten will be missing as he struggles to overcome a muscle injury.
Having been sacked by Schalke last month, relegation-threatened Wolfsburg coach Felix Magath brings his team back to Gelsenkirchen to face the Champions
The mid-table Royal Blues, now coached by ex-Hoffenheim boss Ralf Rangnick, stunned Champions League holders Inter Milan with a 5-2 victory at the San Siro in midweek, while Wolfsburg are third from bottom.
"Of course, this is not quite the same as a match against any other former club of mine," admitted Magath.
"It is still a bit too close to just put it out of your mind."
And Schalke's players still carry the scars of working under Magath.
"Until recently, many players lived in fear of him," said Peru winger Jefferson Farfan in German magazine Sport-Bild.
But captain Manuel Neuer insists the coach issue is not a big deal.
"It is the game between Wolfsburg and Schalke, not Schalke against Magath," the 25-year-old said.