Kingfisher lenders said on Monday the debt-ridden carrier has not informed them of anything concrete after 49 per cent foreign direct investment was allowed in airlines on September 14.
However, an SBI official said lenders are likely to meet the Kingfisher management soon.
This will be the first meeting after the government allowed 49 per cent FDI in domestic airlines.
"We have heard nothing concrete from them after the policy relaxation on FDI.
"Newspaper reports say they are in talks (with foreign airlines to divest stake).
"I am sure Mallya will come to us when he has something tangible," SBI chairman Pratip Chaudhuri told reporters in Mumbai.
Earlier, the 17-member bankers consortium had met in Mumbai and had asked airline promoter Vijay Mallya to personally make a presentation on turnaround plan.
SBI has the largest exposure of Rs 1,500 crore (Rs 15 billion)
Chaudhuri further said that he expects the next meeting in the first half of October.
"The brand Kingfisher is very important for Mallya and the talk of selling non-core assets like Mangalore Refineries is welcome," Chaudhuri said, adding, "Mallya is keen to keep control of Kingfisher...So the sense we have from him is that he is willing to do everything possible, including big sacrifices."
However, an SBI official said the meeting could be early as in the next couple of days.
The airline, which has not reported a single quarter of profit since its launch in May 2005, is sitting on a debt pile of around 15,000 crore (Rs 150 billion) and accumulated losses and is operating a skeletal fleet of under 10 aircraft.
From being the No 2 airline till a year ago, its market share stood at 3.2 per cent in August, the lowest among all the seven airlines in the country.