The France striker struggled to live up to his 35 million euro price tag after joining from Olympique Lyon in 2009 but has looked close to his best in the last month.
A double in the 2-0 win over Hercules in La Liga on Saturday made it eight goals in his last six outings, taking his tally for the season to 19 in all competitions.
"I like to have selection problems and to have to choose, and that nobody has a guaranteed place," Mourinho told reporters at the Bernabeu after Saturday's victory.
"Karim is doing better than ever and is doing things he never did before. We joke that now he is even winning headers at the near post on corners we are defending. He's happy.
"With Cristiano Ronaldo and Gonzalo Higuain out injured he has scored four goals in the last two games to secure six important points (in the league)."
