Mourinho fired the first shots ahead of his clash with the man who replaced him at Old Trafford by ridiculing Solskjaer's suggestion that winning trophies are an ego trip for some managers.
Solskjaer is on course to clinch runners-up spot behind Manchester City in the Premier League title race – three years after Mourinho claimed trailing Pep Guardiola's Centurions by 19 points was one of his finest achievements.
Solskjeer said: “You can't say that (finishing second) is an achievement.
“Our ambition is a lot more than second place.
“I said that when I wasn't even at the club. You can never be happy with that - and we're not.
“Don't get me wrong, our ambition is to catch the team in front of us."