The Cameroon star has become a firm fans` favourite having bagged six goals in just 29 games, including the winner in the recent Tyne-Tees derby against Newcastle.
McClaren confirmed that the club will be talking with Real Madrid about the possibility of securing his permanent signature.
"We're starting to make positive moves about the possibility of keeping Geremi at the club when his contract runs out in the summer," said McClaren.
"We want him to stay and I know the fans have taken to him.
"We've made every effort to make sure he's settled on Teesside and felt at home at the club.
"He clearly likes it here and he's enjoyed the season so far, so that's on our side.
"He's had a very positive effect on the team both on and off the pitch.
"He's obviously a great character around the club and is well liked by his team-mates.
"He's our joint top scorer and only Thierry Henry has more assists than his eight in the Premier League.
"Our next step will be to talk to Real Madrid sometime in the near future."
Madrid are unlikely to stand in Geremi's way in the summer, but Boro may face stiff competition for the African.
A number of English, Italian and Spanish clubs are thought to have - like McClaren - been impressed with his Boro displays.
The Teessiders have already admitted that they will continue to buck the recent transfer trend and will make money available to McClaren.
Boro will hope that Geremi will remain on Teesside, where he seems to have settled very well.
Meanwhile, Boro have a number of injury doubts ahead of their Yorkshire derby clash with Leeds on Saturday.
Juninho (ankle), Franck Queudrue (knee) and Michael Ricketts (virus) are all rated as doubtful for the game at Elland Road and McClaren could be forced to change the side that beat Newcastle last time out.
One player returning to fitness and the squad is Malcolm Christie, who has been sidelined with a stomach bug.
