United have not come close to being champions since Fergie retired in 2013.
Since then United have been through two managers before turning to Jose Mourinho 12 months ago.
Despite winning two trophies in his first season in charge - the Europa League and EFL Cup - Mourinho could only guide United to a sixth-placed finish in the Premier League.
But after signing Romelu Lukaku and Victor Lindelof for more than £100m, Jones is convinced the Red Devils are now equipped to end their title drought.
“This year we definitely have to start challenging for the title there’s no question about it,” said Jones.
“I think we can definitely do it with this squad.
“We are relishing the start of the season.
“We’re definitely a lot stronger this year.
“We’ve recruited well - big Rom up front is a threat and a handful.
“Victor has also come in and looks like he’s been here for five years now.
“We’re positive and looking forward to it.
“Last season was disappointing in the league but we won the Europa League - so that wasn’t bad.”
Goals from Henrikh Mkhitaryan and Lukaku’s first for the club earned United a 2-1 win over Real Salt Lake yesterday on their pre-season tour of America.
And defender Jones is convinced Manchester United now have their old swagger back under Mourinho.
The England star added: “I think slowly, but surely we’re getting that back.
“It’s taken time but I think we are getting there now.
“Hopefully this season, every time another team steps out at Old Trafford, they know they are in for a tough time.
“I think we have seen that last season. We drew too many at home, but we will put that right this season and we are looking forward to it.”
United target Ivan Perisic has been included in Inter Milan’s 28-man squad for their pre-season trip to China and Singapore.
