Some sources claimed the JDS leader held political meetings that he didn't want to in Bengaluru.
Mr Kumaraswamy is expected back on Monday evening, well in time for the counting of votes cast across Karnataka in the Saturday election.
He has said he will be "king" rather than kingmaker, indicating that he counts himself in the chief ministerial race.
On Sunday, a statement by Chief Minister Siddaramaiah telegraphed that the Congress -- expected to reduce its tally -- is already preparing grounds for a compromise with the Janata Dal Secular.
Mr Siddaramaiah said he was ready for another term but he would step aside for a Dalit candidate if the party leadership so wanted.
Asked whether he would simply step aside without protest, he said: "I am not against anybody. You see, even the MLAs (legislators) have to give their opinion, is it not?"
The JDS has so far been non-committal about the BJP as well as Congress. Sources say Mr Siddaramaiah's removal from chief ministership could be a rider for Deve Gowda to extend his support to the Congress. The JDS has said it is the Congress's "responsibility" to reach out if it did not get majority.
If the JDS says it will back a Dalit face, the Congress has G Parameshwara, Mallikarjun Kharge and HC Mahadevappa.
An aggregate of exit polls places the BJP ahead of all parties in Karnataka with 97 of the 222 seats where voting was held. The ruling Congress ranks next with 86 seats and the Janata Dal Secular is predicted to end up with 31 seats. A party needs 112 to form a government.
If the predictions bear out, neither the BJP nor the Congress can form a government on their own, and Deve Gowda and his son may be in a position to set the terms to the two national rivals.
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