Former Nottingham Forest boss McClaren was in charge of Derby from September 2013 until last month.
The Rams reached the Championship playoff final in the 2013-14 campaign, and in the recently concluded 2014-15 campaign they narrowly missed out on a top-six finish.
Clement, who has been brought in to guide Derby back to the Premier League, has suggested that the work done by McClaren will help him next season.
“The team has done well in the last few years and came close to achieving promotion,” the former Real Madrid first-team coach told The Derby Telegraph. “We’ll be looking for that bit extra now to get us there.
"The basics are there and that's part of my decision to come to the club. Derby were sat in mid-table for a couple of years but in the last two seasons the team and the club has grown.
"I know that there is a good squad there and we need to look for that bit extra, on the training pitch or in the backroom staff, alongside the playing squad and support departments, so we can make that step.”
Derby do indeed have a strong squad and would have finished in the top six of the Championship had they not collapsed in the second half of the season.
Injuries were a major problem for the Rams, who do have some very good players who can take them back to the Premier League.
This is Clement’s first managerial job, and it will be interesting to see how he fares in the opening weeks of the 2015-16 campaign.