With only four points from six Serie A matches so far, Inter, given an invitation to visit Mongolia, could be contemplating trips to less exotic places such as Padova, Bari and Brescia if they do not start picking up points soon.
Ranieri made a bright start when he replaced Gian Piero Gasperini, fired after five competitive games in charge, with a 3-1 win at Bologna .
The revival was brief, however, as they slumped to a 3-0 home defeat against Napoli then lost 2-1 at Catania a week ago when new signing Diego Forlan was missing with a hamstring injury.
That has left them level with relegation candidates Bologna and Lecce and only two points clear of bottom club Cesena.
The bright spot for Ranieri has been Inter's European form, with Tuesday's 1-0 win at Lille following their earlier 3-2 victory over CSKA Moscow.
"One swallow does not make a spring but the important thing is to have won," he said after Tuesday's match against the French side.
"The lads are working hard, they are taking it seriously, it's a black period but we want to turn over the page and this result is good for morale."
Inter's troubles have certainly not discouraged Elbegdorj, a self-confessed Inter fan who said he stays up at night to watch their matches.
Elbegdorj visited Inter on Wednesday and suggested that the club could help to develop football in his country, currently a modest 167th in the FIFA rankings.
"There are thousands of Mongolians who are fans of Inter. We are building a stadium for football and we are setting up an academy for youngsters who want to play this sport and we would like to collaborate with Inter," he said.
"We're proud of our history and our conquests. Everyone knows the figure of Gengis Khan. In our country, there are more horses than people, six million horses and three million people. They are the most famous horses in the world. I hope that in the future our country can also be famous for football."
Juventus and Udinese, level at the top with 12 points apiece and both still unbeaten, have home matches, Juventus hosting Genoa on Saturday and Udinese entertaining Novara on Sunday.
Defending champions Milan, in 13th place with eight points and themselves far from convincing, visit Lecce on Sunday.
Like Inter, their form has been better in Europe and Wednesday's 2-0 win over BATE Borisov left them with seven points from three group games and cruising towards the last 16.
