Speaking to reporters, he said there was no need for him to travel to Delhi as he has already had a discussion with Shah and has got his approval for the exercise.
"I will speak to the leadership once again and release the list (of ministers) and expand the cabinet with swearing-in ceremony in three to four days," he said.
The chief minister, who had begun his Davos tour on January 19, returned to the city on Friday afternoon, following which several aspirants met him at his residence.
Yediyurappa, who was anxiously waiting for the high-command's nod to expand his cabinet amid intense lobbying by the aspirants, was keen on getting the approval of Shah last week, ahead of his Davos tour.
Though party sources said he will have to go to Delhi and discuss with new party national president J P Nadda, the chief minister maintained there was no need for him to travel to the national capital.
Earlier in the day, Revenue Minister R Ashoka said the chief minister will hold discussions with Nadda and carry forward the expansion exercise.
Responding to a question on how many legislators who won the bypolls will be made ministers, Yediyurappa said, "You will get to know about it once the cabinet expansion is done, wait till then."
To a question on talks that only seven of 11 legislators, who won the bybolls after they were disqualified, will be made ministers, he said, "There's no truth in that. If there is anything particular, I will think and talk about it, but as I had promised they will get opportunity in the ministry."
Asked about the disqualified legislators who lost on a BJP ticket during the bypoll, such as A H Vishwanath (Hunsur) and MTB Nagraj (Hoskote), amid demand that they too should be inducted, he said "that question does not arise at all."
Also, with the high command reportedly not keen on making all the 11 re-elected legislators ministers, whom Yediyurappa has given assurance, it remains to be seen how things turn out.
Not wanting to react on criticism from a few aspirants, about the delay in the expansion, he said, "It is true that there has been a delay, in three days cabinet expansion will be done. It is my duty to fulfil the promise that I had made to some people, I will fulfil it."
B C Patil (Hirekerur), one among the 11 re-elected MLAs, said they were "pained" because of the delay. He, however, said, "There may be reasons for it. The party leadership and Yediyurappa hopefully will find a solution and distribute power through cabinet expansion
Patil later met Yediyurappa and said the chief minister has assured him about expanding the cabinet soon and that he may travel to Delhi, if required.
As the chief minister has already made it clear that the 11 MLAs will be made ministers, lobbying has been on in the party for the remaining ministerial berths.
Currently there are 18 ministers, including the chief minister in the cabinet that has a sanctioned strength of 34.
The cabinet expansion will not be an easy task for the chief minister as he will have to strike a balance by accommodating the victorious legislators as promised and also make place for the old guard, upset at being "neglected" in the first round of the induction exercise.
He also has to give adequate representation to various castes and regions in his cabinet and also deal with allocation of key portfolios.
Also, disqualified legislator R Shankar, who was not given ticket to contest bypolls but was promised ministerial post by Yediyurappa, openly expressing his ministerial aspirations has added to the chief minister''s worry.
Meanwhile, senior minister K S Eshwarappa said, "If anyone from the current ministry is asked to sacrifice the post by high command or the chief minister, we will have to do it. Not sure whether such a situation will arise or not.
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