With 117 members (including Speaker), BJP can ensure easy victory in two of the four seats.
The party is scheduled to hold its core committee meeting on Saturday, where they are likely to discuss names and convey it to the centrl leadership, sources said.
While Prabhakar Kore is looking for another term, names of former Union Minister Ananth Kumar's wife Tejaswini and party general secretary in-charge of Karnataka Muralidhar Rao, among others, are also doing the rounds.
Umesh Katti, an eight-time MLA, who has been sulking for not being made minister, is also making frantic efforts for his brother Ramesh Katti to be chosen for the Rajya Sabha seat, and had last week held a meeting with a section of BJP legislators from north Karnataka that set alarm bells ringing in the ruling party.
Days after hosting a meeting that triggered speculation about dissidence within the BJP, Umesh Katti along with his brother Ramesh met Chief Minister B S Yediyurappa on Thursday at his official residence.
During the meeting Katti is said to have put pressure on the Chief Minister to consider his brother for Rajya Sabha and clarified that the meeting of legislators was a casual one over meals.
As suspense continues over BJP's pick for Rajya Sabha polls, some within the party expect names to come directly from the central leadership.
Congress, which has 68 MLAs, can win one seat easily.
According party sources, senior state leaders will meet in a couple of days to discuss a candidate for the seat it can win, and whether to support JD(S) for another seat.
While former union minister Mallikarjun Kharge seems to be front runner, there are several other aspirants including former Union Ministers Veerappa Moily and K H Muniyappa, Muddahanume Gowda (who gave up Tumkur LS seat for Deve Gowda as coalition's joint candidate), and those retiring.
JD(S) that has only 34 seats in the assembly is not in a position to win a seat in Rajya Sabha on its own, as minimum 44 votes are required and it will need Congress or BJP's support besides their surplus votes.
Speculation is rife that Congress is likely to support JD(S) if party supremo and former Prime Minister H D Deve Gowda is made the candidate, and in return may seek favour in legislative council polls.
The JD(S) legislature party will meet at the party headquarters in Bengaluru on Friday to discuss about contesting the Rajya Sabha polls, the candidate,and strategy to be adopted while seeking support from another party, sources said, adding that as Gowda has not spoken out about his intention to contest, other names are also likely to be discussed.
Meanwhile, lobbying is also on within the ruling BJP for elections to seven seats of the Legislative Council from the Assembly, slated later this month.
Former MLA MTB Nargaraj, who defected from Congress and lost the bypolls on BJP ticket, met Yediyurappa and is said to have sought for council ticket.
A H Vishwanat, who defected from JD(S) but lost bypolls on BJP ticket, also reportedly met the chief minister with similar intention.
Both aspire to become ministers by becoming MLCs as ten others who defected along with them from Congress and JD (S) and won assembly bypolls have been inducted into the Ministry.