The 44-year-old, who boasts previous experience working with Paris Saint-Germain and Bastia in France, was recruited by Clement in January on a deal until the end of the season.
Less than a week on from sealing their Premier League status for another season, Swansea are keen to tie down Makelele to a long-term contract before the current campaign ends.
"It will be done in the next few days. All the terms have been agreed, he just needs to sign. We are very happy Claude is gong to be staying on," Clement told reporters. "He is very well liked by all the staff and the players here.
"He brings great experience of what it is like to play at a very high level. He has used that a lot with the players. He and all my backroom staff have been fantastic."
Clement was less forthcoming about the future of Borja Baston, however, who he says may still have a part to play at the Liberty Stadium despite netting just once in 18 Premier League appearances.