Mourinho has steered Manchester United through to a first EFL Cup final in seven years.
United also remain in contention for all major prizes on offer to them, having reached the knockout stages of the Europa League and the fifth round of the FA Cup.
Life at Old Trafford looks rosy again after three difficult years under both Louis van Gaal and David Moyes.
And Schmeichel believes Mourinho is the right man for the job – and has praised him for getting the most out of his summer signings.
Peter Schmeichel believes Manchester United are on the right track under Jose Mourinho
Manchester United thumped Wigan in the FA Cup on Sunday
Manchester United's FA Cup player ratings against Wigan
Sun, January 29, 2017
Express Sport brings you Manchester United's player ratings from their FA Cup fourth round win over Wigan Athletic
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Sergio Romero – 7.1
"I think it's been fantastic, I expected it to be another bumpy year. Jose has inherited a squad of players and he will have had to assess every one of them," he told Sky Sports News.
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"He is doing that quicker than I thought he would have done. Plus the four additions in the summer [Eric Bailly, Zlatan Ibrahimovic, Henrikh Mkhitaryan and Paul Pogba] have all been really good.
"We are getting back to a Manchester United way of playing, which I didn't expect so quickly, so I am optimistic for the future."
Peter Schmeichel is impressed by Jose Mourinho's Manchester United
Schmeichel also believes United are beginning to resemble a smoother outfit than they did under Van Gaal last season.
"I think Jose has always tried to protect the lead but it is not in our DNA to [do so], it's to get number two, number three and number four," he added.
"[But] he has sent the players out to get two, three and four. It's great to watch and hopefully it's going to be evolved and developed.
"I would be very disappointed if we are not top four. There is a lot of progress, the team is shaping up and the club is getting back into its own rhythm, its own groove."