The Tigers kick-off their involvement in cup competitions this season with a trip to League One side Tranmere Rovers in the opening round of the Carabao Cup.
Although well aware of the threat posed by Micky Mellon’s side, who have achieved back-to-back promotions in the past two campaigns, it’s a tie that McCann wants to see his side progress from.
“You want to have a good run,” he said.
“At the start of the season when I sat down with the boys I outlined what we want to achieve. Having a cup run was one of the things I asked for.
“If it’s the League Cup, great. If it’s the FA Cup, great. If it’s both then that’s even better.
“This club has been used to cup runs, reaching the FA Cup final and things like that. It’s in the genes.
“It’s never easy going to Prenton Park. Micky Mellon has done a tremendous job there.
“Two promotions in the two years. From the Conference to League Two and now League One.
“They’ve got a real winning mentality there and it’ll be a tough game for us, but we’ll try and go to Tranmere and get into the next round.”
A busy schedule in the opening month of the 2019/20 campaign – and with one eye on Saturday’s league trip to Brentford – means that McCann is likely to utilise his full squad for the clash at Preston Park.
“We’ll probably move the team around a wee bit and give some debuts,” he added.
“We had four or five players that didn’t get stripped at the weekend. That’s the competition now that we’ve created.
“We’re looking forward to getting some of these boys game time. It’s not about giving players a rest but we’re not going to take any risks.”