The slumping team is out to right itself by ending an offensive slump at Talen Energy Stadium.
Following a loss to the Red Bulls on Sunday, coach Jim Curtin said the Union must find consistency.
DiCicco, 68, guided the women's team to the 1999 World Cup championship.
The 2-0 loss was their third in a row.
The forward had a hat trick in an 11-minute span in the May matchup.
The game will be Sunday at Talen Energy Stadium.
The Cup matchup will be the second meeting between the teams in less than two weeks.
The MLS club had a problem with the City Islanders last year. Not this time.
The Union begin their quest to reach the Lamar Hunt U.S. Open Cup final for the third time in team history - and win America's oldest soccer competition for the first time ever.
Jill Ellis received $90,000 in bonus and incentive compensation for coaching the U.S. women's national soccer team to the 2015 World Cup title, less than a fifth of what Jurgen Klinsmann collected for guiding the men to the tournament's second round a year earlier.
The veteran backup will start in Wednesday's U.S. Open Cup game against the Harrisburg City Islanders at Talen Energy Stadium.
Watch highlights of Tuesday's CONCACAF games, which left the United States alone in third place in the standings.
At least 17 workers have died on World Cup construction sites, according to Building and Wood Workers' International, a trade union.
Christos FC, a Baltimore-based amateur team, will take on four-time Major League Soccer champion D.C. United.
The Real Madrid and Portugal star is accused of defrauding Spain's tax office of $16.5 million in unpaid taxes.