The former Premier League champions are due to go up against the Spanish giants in a pre-season friendly this week.
"I think there is a gap there [between United and Barcelona]. But there's a gap for a lot of teams, not just ourselves," Goal.com quotes Phelan as saying.
"Barcelona have been exceptional. They've combined experience and youth and maintained success. The challenge for us is to compete.
"It will take time but we're not that far away. We've been in three European finals and we've won one. Now we're hungry to continue that. Barcelona are the ones to catch."
United are preparing to kick off their fresh league campaign with a visit to Goodison Park when they take on Everton on August 20.