In most circumstances lenders will want to see a minimum deposit of 5% of the purchase price in the form of genuine savings. To be seen as genuine savings the funds must have been held for 3-6 months or accumulated consistently over this time and lenders will want evidence of this in the form of bank statements etc.
Accumulating a 5% deposit can be challenging and you will also need to factor in other purchase costs such as lenders mortgage insurance and stamp duty. This is why a savings strategy and plan is important.
If you are fortunate enough to be able to be able to pay the purchase costs and have a deposit of 20% or more then there is no requirement to demonstrate genuine savings - all you need to be able to show is evidence of the funds required.
Mortgage brokers will help you understand the costs involved and what will be treated as genuine savings - for instance in some cases historic rental payments may be counted. Call me on 0412 973 386 if you would like more information - the calculators section of this site can also has tools that can help you understand the amounts you will need to save.