The club has already denied that it is chasing Rosenborg's Norwegian international forward John Carew.
And Kalou was the latest to be denied by the woodwork as Rosenborg held on.
Rosenborg were now having to defend courageously, and keeper Hirchsfeld did well to block Juliano Belletti.
The Germans are now two points behind Real with Rosenborg third, three points behind.
Michael Essien wasted a good chance by shooting wide before Rosenborg took a shock lead after 24 minutes.
Rosenborg looked to be heading for a valuable away draw with the seven-time winners of the European Cup.
Florent Malouda and Salomon Kalou hit the woodwork for Chelsea, but resilient Rosenborg held out to force a draw.
Rosenborg threatened to spring a surprise when Miika Koppinen turned in Marek Sapara's free-kick at the near post in the 24th minute.
The pre-season signs have been encouraging, and they rounded off their preparations with a 4-0 rout of Norwegian side Rosenborg on Monday.
Press reports in Britain suggested that the final straw came when the club drew against lowly Rosenborg in the Champions League on Tuesday.
Two goals in the last five minutes from Brazilians Savio and Roberto Carlos gave trouble-torn Real Madrid a important 3-1 win over Rosenborg.
Berg has had a fine season with Norway's top side Rosenborg, but his opportunities with the national side have been few and far between.
Rosenborg's superior fitness began to tell as the half progressed and Roar Strand blazed wide before Blayney brilliantly tipped Henriksen's shot round the post for a corner.
Chelsea spent the latter stages camped out in Rosenborg's half, but a combination of good fortune, safe handling from Hirschfeld and stout defending kept Mourinho's side at bay.
Rosenborg wasted a glorious opportunity to double their advantage after 51 minutes when Yssouf Kone set up Alexander Tettey, but he blazed wastefully over the top from 12 yards.
"In those days our game against Rosenborg was part-timers against part-timers although their version of what part-timers meant was entirely different to what our version was, " Jeffrey told the club website.
Semb's problems could have been more severe as, despite earlier fears, he has been able to include the English-based trio of Eirik Bakke, Ole Gunnar Solskjaer and Vegard Heggem, as well as Rosenborg's Roar Strand.
Semb has had to do without Man United's Ronny Johnsen, Oyvind Leonhardsen of Spurs and Erik Hoftun who plays for Rosenborg, while he is giving Jan Derek Sorensen, another Rosenborg player, more time to prove his fitness.
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