In 1934, he was approached by Werder Bremen but, instead of joining them, told the DFB that Werder were dishing out financial offers to players. At that time football was still strictly amateur in Germany (officially) and payments to players were not permitted. The affair ended in the club and some of their officials, players and the team manager being fined and suspended.
With four goals in the 1934 FIFA World Cup in Italy, Conen had been the joint second top scorer with Angelo Schiavio of Italy, behind Oldřich Nejedlý of Czechoslovakia who has 6 goals.
In 1936, Conen’s career was halted due to illness. This kept him away from football for three and a half years. Conen was courageous and battled through to return to the national team on 25 June 1939, against Denmark.
After end of war Conen worked as a coach, in the middle of the 1950s, with Eintracht Braunschweig in the North and Wuppertaler SV in the West. He later coached Bayer Leverkusen,SV Schlebusch and BV Opladen.
- Member of Germany’s squad for the 1934 FIFA World Cup (FV Saarbrücken)
- Matches played for Germany: 28 (1934-1942)
- Goals: 27
1932–1935 1. FC Saarbrücken
1938–1944 Stuttgarter Kickers
1943–1944 → Mulhouse (guest player)
1943–1944 → HSV Groß Born (guest player)
1945–1950 Stuttgarter Kickers
1950–1952 Young Fellows Zürich
- Matches played for Germany in the FIFA World Cup: 4 (4 goals)
1934 World Cup first round: Germany – Belgium 5-2 (3 goals)
1934 World Cup quarter-final: Germany – Sweden 2-1
1934 World Cup semi-final: Germany – Czechoslovakia 1-3
1934 World Cup third place match: Germany – Austria 3-2 (1 goal)