The phrase "is becoming possible" is correct and usable in written English.
You can use it when you are describing the process of something becoming possible or likely. For example, "Great progress has been made in the past few years, and what was once impossible is becoming possible."
As DNA analysis becomes more commonplace, it is becoming possible to have on-site molecular labs to assist in field identifications and preservation decisions.
So, though it is still early days, it looks as though these sorts of gene therapy might eventually become mainstream.Dig deeper: Fixing a body's broken genes is becoming possible (February 2014) Genetic mutations predict which cancers will respond to treatment (June 2012) How gene therapy could make it possible to have three parents (October 2012).
Wireless sensor networks become every day more powerful and ubiquitous, and it is becoming possible to design a network for every purpose.
It is becoming possible to hope that many good reforms will come from the Enron mess.
Satellite pictures show record low ice levels, and navigation is becoming possible for longer periods.
Actually, it is becoming possible to get the Chilean experience for considerably less.
The technique is becoming possible only now, thanks to more powerful microprocessors.
"In tourism there is a saying: 'if people can get there, they will go', and that is becoming possible".
The other thing that is becoming possible is to talk about impacts in a much more regional way.
It is becoming possible for users to see – in real time, on one screen – all their account data at different financial institutions.
In January, the Financial Times proclaimed, "For the first time in history, it is becoming possible to read someone else's mind with the power of science".
