Zlatan Ibrahimovic, 35, is United's 27-goal top scorer of which 16 have been in the Premier League.
No other United player has managed double figures in the league, with Juan Mata on six, Paul Pogba on four and Anthony Martial, Marcus Rashford and Henrikh Mkhitaryan on three each.
Mourinho's side travel to bottom club Sunderland on Sunday on a 20-match unbeaten run in the Premier League.
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But 10 of those games have been drawn and seven teams have scored more than their tally of 43 goals this season.
United's attacking problems were laid bare in this week's goalless stalemate with West Bromwich Albion and 1-1 draw against Everton.
"We have some players that are not really players in love with the goal," said Mourinho. "They are good players and they are creative players, but naturally they're not the kind of guy that's a killer."
Javier Hernandez was sold by Mourinho's predecessor Louis van Gaal to Bayer Leverkusen in 2015 and the United boss believes the 28-year-old is the kind of cold-blooded forward his team needs.
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"The way we dominate opponents in the box at Old Trafford, I think 'Chicharito' (Hernandez) would have 20 goals easily, even coming from the bench for the last 10 or 20 minutes," said Mourinho. "He's the guy that when the ball goes here, rebound there, if the goalkeeper saves it, boom — goal, or if the cross is coming, he anticipates the first-post header — goal.”
Mourinho believes United's other attack-minded players have been unlucky in front of goal.
"The number of times Paul Pogba hit the posts are almost Guinness Book of Records," he said. "It's not a problem of quality at all, it's luck. Many goalkeepers become phenomenal at Old Trafford, so give credit to the goalkeepers."
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Mourinho has handed chief executive Ed Woodward a list of four strikers he would want as first choices, along with a list of four 'second picks' for the close-season.
"Are we going to buy a striker? Maybe. But we believe in Marcus (Rashford), no doubt," he added.
Meanwhile, Mourinho admits United couldn't have kept Jesse Lingard had they not agreed to pay him £100,000-a-week.
United offered the 24-year-old England international a new deal to 2021 despite him only being a squad player, with just 12 Premier League appearances this season.
"First of all, if you don't pay, they go," said Mourinho. "We can be criticised for paying so much, but we'd also be criticised if we lost a young English player made in the academy. So the club and the player tried to find a situation that makes everyone happy."
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