|Date of birth||15 February 1964|
|Place of birth||Faroe Islands|
|ÍF Fuglafjarðar (Manager)|
|1986||IK Grand Bodø|
|1999 – 2000||IL Jotun|
|* Senior club appearances and goals counted for the domestic league only|
A fine dribbler boasting a powerful shot, Reynheim played semi-professionally in Norway. Also, he played 110 matches, scoring 32 goals in all competitions for HB Tórshavn and he played for B36 Tórshavn.
Reynheim made his debut in an August 1988 friendly match against Iceland, the country's first FIFA-recognized match and earned 27 caps and 2 goals between 1988 and 1995. His last international was a November 1995 European Championship qualifying match against Greece.
- Scores and results list Faroe Islands' goal tally first.
|1||1 May 1991||Windsor Park, Belfast, Northern Ireland||Northern Ireland||1-1||1-1||1992 Euro qualifying|
|2||5 August 1992||Svangaskarð, Toftir, Faroe Islands||Israel||1-0||1-1||Friendly|
- Kari Reynheim at Footballdatabase