The 85-year-old former union minister had joined the BJP in March last year, praising the leadership of Prime Minister Narendra Modi and BJP chief Amit Shah.
It's not clear what triggered the rumours but some reports suggested that Mr Krishna, a former Karnataka Chief Minister, was unhappy with his daughter not getting a BJP ticket.
In January this year, Mr Krishna had ruled out speculation that he was seeking a BJP ticket for his daughter Shambhavi, saying he was against dynasty politics.
Last year, the BJP had inducted Mr Krishna, an influential leader from the powerful Vokkaliga community that could decide the electoral fortunes of the party in the Mandya, Mysore and Tumkur regions.
Mr Krishna has already made it clear he would not contest elections but would ask his supporters to support the BJP. Karnataka votes on May 12.
While Chief Minister Siddaramaiah refused to comment on the speculation of Mr Krishna's return, state Congress sources told NDTV there was no such move.
The BJP that is eyeing to regain power in the state blamed the rumours on the Congress.
"It is a planted story by the desperate Congressmen who have now realised the worth of Mr SM Krishna. When he quit the Congress party, they made all kinds of allegations, insinuations against him. And the same people are today facing the defeat in the Assembly polls and are remembering SM Krishna," BJP Spokesperson S Prakash told NDTV.