Konsel started his professional career with First Vienna and moved to local rivals Rapid Wien in 1985. He then played a part in the successful Rapid team in the 1980s, claiming the League crown twice and most prominently losing the UEFA Cup Winners Cup Final 3–1 against Everton in Rotterdam in 1985. He stayed at Rapid for 12 years and captained the side in his last two seasons. In 1996, he played in the UEFA Cup Winners Cup Final for a second time, this time against Paris Saint-Germain in Brussels, which Rapid lost again, this time by a score of 1–0.