Drogba, who departed the Blues in 2012 after eight years at Stamford Bridge, has returned on a one-year deal following the expiry of his contract at Turkish outfit Galatasaray.
The 36-year-old hit 157 goals in 341 appearances during his first spell in West London and holds legend status at the club having netted the winning penalty in the 2012 Champions League final.
Drogba linked up with the squad but did not play a part in Chelsea’s 2-1 pre-season friendly win over Slovenian side Olimpija Ljubljana, and Mourinho says it was as though he had never been away.
"First of all when he came, it looks like he never left the club. It was so normal, nothing new at all because he knows everybody and everybody knows him," he told the media after the game.
"He was ever present even when he wasn’t here. Chelsea belonged to him, even in the last two years when he was away playing in a Galatasaray and Shanghai shirt.
"So it looks like he just went for a short holiday and came back, so everything is normal. But yes, I think we need him. We need him as a player for our squad to be the way I like.
"I like my squad with different qualities, not just as football players but also in terms of personalities. I like to have players with different personalities.
"So as a player and person, Didier is somebody we need to be strong."
Fellow summer signing Diego Costa was on the scoresheet in Slovenia, latching onto Cesc Fabregas’ through ball to fire home an equaliser, before Kurt Zouma added a winner from close range.
It was a first run-out in Chelsea colours for the new pair, who joined from Atletico Madrid and Barcelona respectively, but Mourinho was reluctant to get carried away by their bright start.
"It’s nice for Diego to score – but no more than nice. And for Cesc, it’s important step-by-step for him to understand the team," he said.
"But we will not see the best of them until we have all our creative players back.
"We don’t have Andre Schurrle, Willian, Oscar or Eden Hazard. Only when they are back can we assess things properly."
Mourinho also admitted he was grateful to face testing opposition in pre-season, taking what has been interpreted as a sly dig at Manchester United following their 7-0 win over LA Galaxy.
"At the moment, this is a training camp against teams far more advanced in fitness than us and our objective is to try to compete," he said.
"To win 6-0, 7-0 or 8-0 is not good enough for us in preparation for the new season.
"We want difficult conditions and situations for our games.
"We feel we are going to be very strong and we want to fight for the title. Every team has got stronger."