Reports seen by the mayor show transport bosses at Sheffield City Region are concerned around the sale of FirstGroup. The UK operation is said to be ‘unprofitable’.
Transport chiefs working under Mr Jarvis said there could be "substantial bus service reductions" without "significant public subsidy".
First operate over 400 buses in Sheffield, Doncaster and Rotherham – around half of the total South Yorkshire fleet – as well as other areas, including around Leeds.
City region bosses go on to say there are now ‘limited options’ in combating bus pressures while delivering further savings "without compromising the quality of public transport services".
Mr Jarvis also said bus services are "not as good as he’d like them to be" and unlike train operators, the state are not automatically on hand to take over failed services.
The mayor has called on the government for more resources for devolved areas to invest in bus services.
Steel firm Liberty planning 280 job cuts in South YorkshireNorthern Rail could be nationalised 'within months', says Transport Secretary Grant ShappsMr Jarvis said: “The difference between rail and buses – the railways have the operator of last resort so that government has the ability to step in and underwrite an take on services where the operators have failed.
“That same option doesn’t apply to bus services – I’m incredibly mindful of the pressures of on our bus network in South Yorkshire and that’s why it’s incredibly useful Clive Betts is undertaking this bus review, going round the country and looking at best practice.
“South Yorkshire has traditionally – going back a generation – has had a good reputation in terms of buses but we’ve seen quite a rapid decline in passenger use in recent times.
“I’ve put a huge amount of effort into the issue of transport, we’ve got a dedicated transport board, we’ve got a much better relationship with our local authorities and national government which wasn’t the case previously.
“There is a real energy about what we’re doing but what I don’t have is the one thing I really need which is the additional money and resources to put into the system.”