During Euro 2000, the 23-year-old was Denmark's most dangerous player, with his attacking surges down the left wing the one bright spark for the Danes, who crashed out of the competition without registering a single point.
Gronkjaer embarked upon an average of 12 dribbles per game in the lowlands - more than any other player in the tournament - and was clearly Denmark's danger man in the absence of the Laudrup brothers.
The Ajax midfielder also whipped in 12 centres during Euro 2000 - more than any of his team-mates - to indicate that he could be the man to provide more ammunition for Chelsea's forward line.
He was also confident enough to go for goal himself when the opportunity arose, forcing saves with two of his three attempts on goal.
After his exciting performances, it was reported that Chelsea had tabled a £7.8 million bid for Gronkjaer's services, but the deal appeared to go cold and many of Europe's top clubs came courting, with Barcelona considered the favourites to snap up the winger.
However, with Chelsea short on attacking options on the left wing, it seems that new boss Claudio Ranieri has earmarked the Danish starlet as his main transfer target and could pip the Catalan club to Gronkjaer's signature with a renewed bid.