"The Superstar has recovered but we want him to stay in Singapore for at least a week so that he has more privacy, " said the Tamil actor who married Rajinikanth's daughter Aishwarya in 2004.
"He is on a normal diet, is cheerful and is spending time walking, watching films and meditating, " Dhanush told reporters.
"The Superstar's health condition is super, and if he doesn't return in 10 days, it means he is enjoying a vacation there, " he said.
He thanked all Rajini fans for their prayers and wishes.
"Thank you guys. Its really touching dat u all r wid us.V all need you and ur prayers r all answered well :), " tweeted Dhanush.
The actor also cleared the rumour on 'Rana' being Rajinikanth's last film.
"I never said rana s sirs last film. Wen asked whether he ll cont actin n movies I said dat only he shud answer but rana wil happen.god bless, " Dhanush he posted on micro-blogging site Twitter.
"Its really funny how pple can manipulate statements. Haha. Oh I'm tired of this rumours now :) I never made a statement like that. Its absolutely made up news. Rajini wil keep rocking, " he tweeted as he joined Rajinikanth in Singapore.
Rajinikanth has been admitted to Intensive Care Unit (ICU) at Mount Elizabeth Hospital, where he is reportedly being treated for kidney ailment.
The Tamil actor, in a one-minute audio tape, said: "I am happily going about my routine. I will return as soon as the treatment is over."
Thanking his fans for their love and support, he said: "How can I reciprocate the love you have shown for me? How will I pay you all back? I will never let down all my fans throughout the world. I have God's blessings and the blessings of the Guru. Above all, I have the blessing of all my fans who are the manifestation of God."
Rajinikanth flew to Singapore for treatment on Friday night along with daughters Aishwarya and Soundarya, sons-in-laws and doctor Muralidharan. His wife Latha joined him on Saturday.
Rajinikanth was admitted to Sri Ramachandra Medical Centre on May 15.
The Tamil actor has been undergoing dialysis and has kidney problems.
Rajinikanth has been suffering from recurrent respiratory infection and gastro intestinal ailments and was advised complete bed rest.
The 61-year-old star with a god like fan following after the phenomenal success of Robot (Endhiran), which was dubbed in Hindi as well, had recently started working on his new film Rana with Deepika Padukone in Chennai.
He plays three roles in the film on the Mahurat sets of which he fell sick on April 29 and had to be hospitalized first.