The veteran singer was admitted to Breach Candy hospital here on Monday after suffering a chest infection.
Ace filmmaker Madhur Bhandarkar also tweeted about her condition and urged people not to spread baseless rumours.
"Just spoke to the family. #LataMangeshkar Tai is stable and recovering. My humble request, not to spread baseless rumours and pray for @mangeshkarlata speedy recovery," he tweeted.
Lata Mangeshkar, who began her career in 1942 is a recipient of the Bharat Ratna, Padma Vibhushan, Padma Bhushan and the Dadasaheb Phalke Awards.
She is known for iconic songs "Aye mere vatan ke logon" and "Babul Pyare" among others. She has sung over 25,000 songs in over 20 Indian languages.