The Rams have won eight of their past 10 games, the only defeat being Wednesday's loss to Wigan, to sit in promotion contention in fourth place in the Sky Bet Championship.
Former England boss McClaren is capable of re-establishing Derby in the Premier League, according to Mourinho, who is sending a first-choice team to the newly-named iPro Stadium to tackle the Rams.
Mourinho told Chelsea TV: "He knows the football that can take him not just to the Premier League, but also to play with a certain stability if, or when, they reach the Premier League.
"A team that will play the best they can, without any kind of pressure.
"Do we lose? Do we win? Who knows? At least the message is we respect them and we go there with the best possible team.
"The next game after Derby is Hull at the weekend. We can play against Derby and have a day off on Monday.
"It's the last game of this crazy 15 days. After that things come back for normality for a couple of weeks.
"I think the players are also keen on it, to go, go with a strong side and at least tell our opponent that we are going there with maximum respect."
Chelsea begin the FA Cup in a strong position in the Premier League, third, two points behind leaders Arsenal, following a good festive run which has left Mourinho satisfied.
He said: "Good results, good performances. Being there. Not top of the league, but very close to it. In a good position. I'm happy."
Now attention turns to a competition the Blues have won in four of the past seven attempts.
"It's a fantastic competition," Mourinho added.
"Chelsea won lots. Two of them are unforgettable, because Chelsea won the last in the old Wembley (in 2000) and the first at the new Wembley (in 2007). Two historical moments."
The 2007 win was Mourinho's most recent Chelsea trophy, coming four months before the end of his first spell as boss.
The next bid to win the FA Cup begins at Derby.
David Luiz is available following suspension, but midfielder Frank Lampard and right-back Branislav Ivanovic are out until the end of the month.
The injury to Ivanovic offers Cesar Azpilicueta a run of games in his favoured right-back berth, after he impressed so much out of position on the left flank that Ashley Cole was unable to dislodge him.
"Obviously I'm used to playing as a right-back but when the manager asked me to play at left-back I just wanted to do my best," the Spain right-back told chelseafc.com.
"The role is very similar, although of course there is more need for me to use my left foot.
"Because competition within the squad is very high, when you play, in any position, you feel good, and you just want to do everything you can to help the team."
Azpilicueta has learned from working alongside Cole and Ivanovic.
"It's amazing for me to work every day with Ashley and Branislav," he added.
"Since I've been at the club I've learnt so much from them because they are top players and top men.
"I have a very good relationship with them both and I try to take as much as I can from the way they play.
"I have a chance to work alongside them regularly which helps me improve, and for the national team I'm in the same position.
"It's important for every player to always try to improve, I watch these players very closely and I think it's helped me so far."