Their improved form since the departure of Jose Mourinho in December has seen United overhaul Chelsea and Arsenal in the table and move into fourth place on 51 points.
They also claimed a 3-1 FA Cup win at Emirates Stadium last month and will now meet Chelsea at Stamford Bridge for a place in the quarter-finals.
Zola, who earned his coaching badges alongside Solskjaer, is happy to see the former striker having such a positive impact in a difficult job.
"I am pleased, first of all," he told a news conference. "That is the first feeling that I have. I know Ole, we did the course together and I am pleased to see him doing so well.
"I knew that United weren't going through a very good moment before, but I knew the value of the team and they were going to come back.
"What Ole has done in this small amount of time is quite remarkable. He was clever, he was always interested, and you can see when someone is focusing on what they do."
Despite the loss to PSG, Zola believes United's players are enjoying their football more, which makes them daunting opponents.
"It's a classic, it's a great game," he said. "They are in a good moment and it's the sort of challenge we need right now.
"You can see they are a team at the moment who are enjoying what they are doing. They are committed, they are working as a group.
"When you have this attitude and the qualities that they have it can only be good.
"The only thing you can say is they had a very good coach before and sometimes things don't work out. The value of the team wasn't in doubt before and it is not surprising now that they are doing what they are doing."
Chelsea have won the last four cup meetings between the two teams, including last season's final, but Zola admits he did not always enjoy playing against United under Alex Ferguson.
"I have fantastic memories of him – not when I played against his team – but respect, great respect for the person and the manager," he said.
"He used to like to mark me with [Gary] Neville all the time. It was not very pleasant for me. I didn't like it.
"It’s always been a fantastic game, very competitive. It's a game that both sets of supporters feel a lot."