The former Manchester City man believes the Red Devils will make it through to the knockout stages.
United face Basel tomorrow night at Old Trafford, with Benfica and CSKA Moscow also in their group.
“Our sides probably haven’t gone as deep as we probably want them to, I think that’s maybe due to the level of competition week in, week out in the Premier League,” Barton told talkSPORT.
“We are due a little period, remember a few years ago when Chelsea, Liverpool went on to win it, Man Utd were in a final a couple of times.
“I think we are due another little period, Barcelona aren’t as strong as they once were, Real Madrid have had a little bit of a tough start, Bayern are in a bit of a transition phase, obviously PSG spending, but you have to put all our big clubs, City, United, Chelsea, Spurs, Liverpool in that bracket.”
Barton thinks the top clubs across Europe will want to avoid United in the knockout stages.
He added: “They (United) will be there or thereabouts. I expect them to get out of the group.
“Such as the level of competition in European football right now that once you get out of the group, you’ve got to get a bit of fortune or get on the right side of the draw.
“Before you know it you can be into the quarter-final.
“I think Man Utd are in really good fettle so I expect them to progress from the group because they’ve got a decent group.
“After that I think they will be there or thereabouts. They will be a tough team to beat, I don’t think any team will want to draw Manchester United in the knockout stages of the Champions League.”
United are back in the Champions League after winning the Europa League last season, beating Ajax in the final.
