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.
"I am very, very confident the Congress party will get a clear majority and I hope I will be the chief minister... If they want to make a Dalit a Chief Minister, I don't have any objection," he told reporters.
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?"
It is well-known that Deve Gowda has still not forgiven Siddaramaiah for joining the Congress after exiting the Janata Dal Secular in 2006. A founder member of the JDS, Siddaramaiah was upset with his party over Mr Kumaraswamy's rise by dint of being Deve Gowda's son.
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.
Speaking to NDTV, Mallikarjun Kharge said: "I will not respond to a hypothetical statement. It's for the high command to decide. We fought the election under the leadership of Siddaramaiah... why do you look at me as a Dalit leader?" He also expressed confidence that the party would win a full majority on its own, and not need the JDS.
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.