Mongolian officials have made particularly bullish comments in recent days, with a senior figure in the mining ministry Otgochuluu Chuluuntserent saying over the weekend that a resolution was just days away.
But multiple lenders indicated on Monday they were not expecting a full resolution of the issues in time to meet the September 30 deadline.
Several of the 15 international banks involved in the deal said they would be happy to extend their funding deadlines once again, having been encouraged by the recent improvement in relations between the two camps.
The lenders said they were increasingly confident a deal could be solved by the end of the 2014 calendar year.
The European Bank for Reconstruction and Development, which is part of the funding group, confirmed that its deadline was already set at December 31, rather than September 30.
Rio chief executive Sam Walsh has previously likened his company's relationship with Mongolia to a long marriage, and has said he is willing to miss short-term funding deadlines to make sure the terms of the relationship with the developing nation were right.
"We are not about rushing to meet a deadline," he said in March.
If Rio does surprise by resolving all issues before the September 30 deadline, the biggest winner could be the shares of Turquoise Hill Resources, the Canadian subsidiary of Rio that holds Rio's interest in Oyu Tolgoi. 
Shares in Turquoise Hill have surged in recent weeks on the back of the thawing relationship between Rio and Mongolia.
Turquoise shares were fetching $C3.57($3.67) in September, but reached $C4.42 on September 15.
They slipped back to $C4 last week, only to spike again on Saturday morning Australian time to be $C4.26.
Rio's shares, which are far more responsive to the direction of the iron ore price, have fallen sharply over the past two months.
The stock fell another 90 cents on Monday to be fetching $59.21- Rio's lowest share price since late June.