United finished sixth last season but did qualify for the Champions League by winning the Europa League.
If United are to be serious title contenders, being more clinical at Old Trafford should be a priority for Mourinho, starting with the home match against the Hammers.
Other star players to watch out for in the competition this season include Manchester United's new Sh10 billion signing Romelu Lukaku, Arsenal new signing Alexandre Lacazzette, Liverpool's Brazilian playmaker Coutinho and Chelsea's new Spanish forward Avaro Morata.
But a Premier League title challenge is required this time around, with Lukaku providing a powerful presence in attack to replace the injured Zlatan Ibrahimovic.
Mourinho knows they were over-reliant on the injured striker's goals and wants more support for this season's main man, Romelu Lukaku.
"So I'm convinced I have - not just the hope - but the conviction that our second season, in terms of the quality of our team, is going to be better". Star signing Pogba struggled to live to his full potential (and price tag), with only five goals and four assists in domestic football.
Midfield: Nemanja Matic is set to make his league debut for United following his move from Chelsea after impressing against Madrid in midweek and the Serbian should start alongside Ander Herrera in the middle of the park. Victor [Lindelof] can play right-back, centre midfield.
"We are going to try to give a hard fight to the top teams in Europe in the Champions League". Eric Bailly, bought a year ago for £30m, and Antonio Valencia, are the only two defenders who look assured of a starting spot. As stingy as United's defence was last season - Mourinho's team kept the joint most clean sheets in the league with 17 - they can at times look really shaky at the back and will need to avoid conceding late goals. Sergio Romero represents a solid second choice, who is happy to step up when called on.
"But I was not thinking of him because I never go to players who I think are the impossible mission".
He said: "In many ways, it is my team".
"It is not because I have always done it (won the league title in his second season) that I am going to do it again", Mourinho said.
Manchester United's opening six matches are against West Ham, Swansea City, Leicester City, Stoke City, Everton and Southampton and a strong start is a must for Mourinho and his men.
However, the United manager is confident that his team can improve on that, having had a good pre-season and are well prepared.
If Mourinho is feeling the pressure of maintaining his record of winning league titles within two years at Porto, Chelsea (twice), Inter Milan and Real Madrid, he's not showing it.
Since taking over the reins at the Manchester club, the Portuguese manager has spent over £300 million and meticulously cherry-picked his signings.
However, the club did win the Europa League and the League Cup, giving the manager a platform of success on which to build.
After only finishing sixth previous year, England's most decorated football club will be looking to get back into the top four, and mount a serious title charge for the first time since Sir Alex Ferguson left the club. Anything less would be considered failure.