There have been instances when Asim desired to be the captain of the house.
Firstly, during the sacks and cartons delivery task. Asim wanted to be the captain at that time. But Shukla didn't support him and gave the names of the girls to be the contenders although Asim performed the task really well.(it wasn't shown in the episode, you can watch the unseen video for reference)
Secondly during the rakhshas task,we had seen Shukla openly supporting Vishal for captaincy. He didn't even mention Asim's name for captaincy.
And yesterday,when again there was an opportunity for Shukla to make Asim ,the captain of the house,he again betrayed him and took Vikas Gupta's name. Although Paras suggested Asim's name because Asim did perform well. But Shukla is Shukla,he can't see Asim as a captain.
All in all,Asim was never in the priority list of Shukla although he called him his Bhai, friend etc. etc.