United picked up three pieces of silverware in 2016-17 with the Community Shield, EFL Cup and Europa League triumphs getting the Jose Mourinho era off to positive start, although they failed to challenge for the Premier League title.
The Red Devils find themselves in the Champions League this season and will be hoping to enjoy a stronger campaign domestically following further additions to the squad this summer.
Carrick feels United must look to build on the solid foundation put in place last term and insists they are capable of challenging on a number of fronts.
“It is difficult to say what our chances in the league are but we are setting out to be on top,” Carrick told the United Review.
“We have certainly improved the squad, we look stronger, we are a year further ahead with the manager and his staff, we are in a better place than we were last year, so things are on the up.
“For large spells of last season, we felt we should have been higher up in the league than we were and performances certainly warranted that for large periods as well.
“But it is too easy to sit here and say that. We need to improve because we ended up a distance away from the top. Hopefully this season we will be right up there challenging.”
Punters using their free bet may want to back United to make a winning start to the 2017-18 season when they host West Ham on Sunday.