The Red Devils finished in second place in the Premier League table last term behind runaway champions Manchester City.
Jose Mourinho’s side secured their best finish since the Sir Alex Ferguson era when Manchester United won their 13th top-flight crown.
Manchester United signed three players in the 2018 summer transfer window but missed out on some of Jose Mourinho’s targets.
The Red Devils lost successive games to Brighton and Hove Albion and Tottenham Hotspur before beating Burnley and Watford.
Mourinho’s side are eight points adrift of leaders Liverpool FC following their 1-1 draw with Wolves at Old Trafford on Saturday.
Former Leicester star Savage is backing Manchester United to end up in fourth spot behind Man City, Liverpool FC and Chelsea FC.
“You’re six [now eight] points off the leaders,” Savage told BBC Sport. “I think it will be a top four finish this season.”
Manchester United signed Diogo Dalot, Lee Grant and Fred in the 2018 summer transfer window to bolster Mourinho’s squad depth.
The Red Devils lost 1-0 to Chelsea FC in the FA Cup final at Wembley following Eden Hazard’s winner from the penalty spot.
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