Asante joined her first club Arsenal as a junior in 1998. She became a senior player in 2003/2004 season. Asante was part of the Arsenal team that won the quadruple in 2006/2007, collecting the UEFA Women's Cup, FA Women's National Premier League, FA Women's Cup and the FA Women's Premier League Cup. Asante was part of the Arsenal team that made history by being the first team outside Germany or Scandinavia to win the UEFA Women's Cup. Asante is reported to have played exceptionally well in the final.