The left-back, who joined the club from Southampton in 2014, endured a mixed debut campaign, making 16 Premier League appearances as the club recorded a fourth-placed finish.
And Shaw believes Louis van Gaal’s men are capable of improving their league position and challenging for major honours this time around, having recruited Bastian Schweinsteiger, Morgan Schneiderlin, Memphis Depay, Matteo Darmian and Sergio Romero this summer.
"As a team, we do talk about challenging for honours, but not too much because it is the start of the season," he told the club’s official website.
"But with the signings that we have made and the signings that could still be coming in, I think the squad is going to be very strong and positive, and I think we can win a couple of trophies this season."
Chris Smalling has echoed Shaw’s sentiments, meanwhile, and believes that the club’s new additions will help inspire the Red Devils to success this term.
"I feel the fans can expect to see a team that shows a lot more consistency and, especially with our additions, I think we will see a big goal threat in a successful season. Everyone is very confident of building on last season," he added.
