Hamann feels Mourinho’s better squad and the Portuguese’s calmer attitude is behind the 20-time Premier League club’s turnaround in form, having won eight games on the spin now.
They currently sit sixth in the Premier League table but are just three points behind Tottenham in third.
Hamann told Sky Sports: “There was a time a few weeks ago when United had a seven or eight-point gap to fourth place, and the deficiency now is three points.
“They’re in touching distance with all the other teams apart from Chelsea, so Mourinho is a lot more safe.
Referring to incidents earlier this season, such as Mourinho’s public criticism of United players Luke Shaw and Chris Smalling as well as several FA sanctions for misconduct, he added: “[Mourinho’s] behaviour was a bit erratic at the start of the season, and he took a step back for whatever reason.
“Perhaps someone at the club had a word with him and said at Man Utd he can’t get away with things he may have done at other clubs. I think that’s part to do with the form they’ve found, they look a far happier outfit.”
Hamann spent seven years with the United’s big rivals after joining from Newcastle in 2009 and lifted several trophies at the club including the Champions League in 2005.
The ex-Germany international added: “At the start of the season I tipped him to win the Premier League. Whether a 10-point lead for Chelsea is too much I’m not sure, but I still believe United have the most talented squad and once Mourinho’s teams get going they can be very hard to stop.”
United have won their last six games and remained unbeaten in their last 11 to cut the gap between them and Manchester City in fourth to just three points after 20 league games.
Klopp’s men have been equally impressive this season, winning four of their last six games to go second in the league – five points behind leaders Chelsea.