Lukaku scored on his competitive debut for United in Tuesday's 2-1 UEFA Super Cup defeat to Madrid in Skopje and was named in Mourinho's starting line-up alongside Matic to make his Premier League bow against Slaven Bilic's side.
Sky Sports report the Man United boss said: "I want to play West Ham a hard match, then go to Swansea for another hard match". Despite making the ideal start on the opening day, the Reds finished the season in third place, surrendering the title to Arsenal's "Invincibles", who went the entire 38-game league season unbeaten.
Asked by MUTV if he could have hoped for more, Lukaku replied with a wry smile: "I wished to have three goals and a hat-trick to be fair, that would have been nicer".
Hernandez won two Premier League titles during his time at United, the second of which came in 2013 as Sir Alex Ferguson retired in style by delivering another trophy for the club. I was thinking, three transfer windows, I need that.More news: 'N Korean missiles can reach Guam in 14 minutes'
The Hammers have significantly strengthened their lineup in between two seasons, but it did not help them much in getting a successful pre-season campaign and they won't visit Old Trafford in the best of the moods. Hammers have better players at every line. "Hopefully this season we will be right up there challenging".
"We're going to try to win the title".
He added: "It depends on what is happening or what was happening behind doors and we don't know. They can still be like new players for us later in the season, so we are fine".
"I am very happy and glad, it's the best way to come back and open at Old Trafford".
But Neville, a former household name at Old Trafford, now believes United are in a position to win English football's top prize once more this season, particularly after the investment they have made into the team.More news: Congress seeks UP CM Yogi Adityanath's apology over Gorakhpur deaths
The Belgian struck in the 33rd and 52nd minutes, first getting on the end of a flawless through ball from Marcus Rashford and then heading a second goal from a drifted Henrikh Mkhitaryan free kick after the break.
"But I think the performance based on the confidence levels was really high".
And the Armenian made it two assists for the day a few minutes from time as he played in substitute Anthony Martial with a handsome first-time pass.
"For all of Zlatan Ibrahimovic's qualities, he could not offer United a threat running behind defences given his age and Lukaku will bring that to them now", BT Sport presenter Lineker told Independent.ie in an exclusive interview.More news: Fargo Public Library to host two solar eclipse events
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