The two clubs will meet at Old Trafford in the first leg of their last-eight clash on Wednesday, with the return fixture scheduled to take place next week.
Barcelona are favourites to progress to the semi-finals as they chase a treble come June, while the competition represents United's last hope of silverware this term.
Messi has spearheaded the Spanish champions' trophy assault once again, scoring over 40 goals across all competitions this season.
Pogba, meanwhile, has been a fixture in the Red Devils' starting line-up and, despite a recent loss of form, his overall record for the campaign so far reads 14 goals and 10 assists from 39 appearances.
Ibrahimovic, who spent two years on Barcelona's books between 2009 and 2011, while also enjoying a two-year spell at United from 2016 to 2018, has highlighted the influence of the mercurial pair ahead of kick-off in Manchester.
"Two big teams, two big clubs playing against each other," the Swedish striker told Barca's official website. "Two clubs with great history and it will be exciting to see.
"Obviously, Messi makes the difference in each game he plays, it's no secret.
"I think for United, you have Pogba making the difference there. It will be more of a battle between Messi and Pogba, even if it's a collective sport."
Solskjaer's men head into the match off the back of three defeats in their last four outings, having most recently suffered a 2-1 lost in the Premier League at Wolves on April 2.
Barca, meanwhile, have won five of their last six and moved one step closer to retaining the Liga title with a 2-0 win over Atletico Madrid on Saturday.
Ibrahimovic, who now plies his trade in the MLS with the LA Galaxy, went on to share memories from his time at Camp Nou, stating: "Barca was the best team in the world. Everywhere we went, people had so much respect for us and you enjoy playing in the team.
"You had a feeling you would win any game even if you were not performing at the top level because the team was so strong. Great memories."