The Red Devils have endured a mixed week in the build up to the fixture, as they were knocked out of the FA Cup on Monday night by Chelsea, before progressing through to the quarter-finals of the Europa League thanks to their 2-1 aggregate success over Rostov.
Jose Mourinho's men must now turn their attention back to Premier League action and England international Jones believes his side will face a tough trip to the North East, particularly as Boro parted ways with boss Aitor Karanka this week.
Jones told MUTV: "Middlesbrough have just sacked the manager as well so it will probably be even tougher than what it would have been."
United will head into the match without suspended duo Zlatan Ibrahimovic and Ander Herrera, while Paul Pogba has been ruled out with a hamstring strain and there are also doubts over Wayne Rooney, Luke Shaw, Daley Blind and Anthony Martial.
Despite United’s growing list of absentees, coupled with Boro's change in manager, Jones is still convinced his side still have enough strength in depth to secure all three points.
He added: "We’ve got more than enough to cope with that. We have strength in depth in this squad and that’s why we need everyone."
The Manchester giants are unbeaten in their last eight league meetings with Boro and punters may choose to use their free bet to back Mourinho's men to continue that run on Sunday.