United boss Solskjaer is yet to win anything since taking charge at Old Trafford nearly two and a half years ago. He had claimed trophies can act as an "ego thing" for some managers and that building foundations for long-term success was more important to him.
"Sometimes a trophy can hide the other fact of what's happening at the club," Solskjaer said last month.
"It's in the league position you see if you're progressing, really."
However, Tottenham manager Mourinho, who won two major trophies in less than three years in charge at United, doubts Sir Alex Ferguson would be in agreement with Solskjaer.
Mourinho said: "It's his opinion. I'm pretty sure his big boss Sir Alex had a different opinion about it. But I respect what Solskjaer thinks. I think different.
"Freedom of thinking, freedom of ideas, and if that is what he thinks that is fine by me. It's not a problem for me, he's not being disrespectful to anyone.
"But I repeat I believe his big boss, and the biggest in Premier League history, has a different view in relation to that."
Ferguson is the most successful manager in Premier League history and won 38 trophies in 26 years in charge at Old Trafford, including the Treble in 1999.
Solskjaer takes his United team to Spurs on Sunday looking to avenge the 6-1 loss at Old Trafford earlier in the season.
The Red Devils have since recovered to move up to second place in the table, while Spurs sit in seventh spot.
Meanwhile, Solskjaer has told his United's players to keep their composure on Sunday.
Anthony Martial was sent off in the 28th minute in the October defeat after retaliating to an elbow from Erik Lamela with a push in the Argentinian's face.
"When you sign for #MUFC these are the games that you look forward to."- Sky Sports Premier League (@SkySportsPL) January 13, 2019
Ole Gunnar Solskjaer speaks ahead of @spursOfficial v @ManUtd live on Sky Sports Premier League at 4.15pm.
Watch in-game clips and highlights with the Sky Sports app: https://t.co/qSgl6MG3Fg pic.twitter.com/Ee1XKzrdbU
"We got conned into a red card and that's something we have to be aware of," Solskjaer said. "We can't react, because in games there'll be situations you'll be wound up; we've learnt from that.
"I think the players will remember that game with a lot of pain and their pride has been hurt. Pre-season was short ... but we were so poor and I'm sure we'll see some players wanting to prove we're better than that."
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