The phrase "a growing possibility" is correct and usable in written English.
It can be used to describe an increasing likelihood or chance of something happening over time.
Example: "With the recent developments in technology, there is a growing possibility that we will see significant advancements in renewable energy sources."
Alternatives: "an increasing likelihood" or "a rising chance".
A Canada-Russia gold-medal game is a growing possibility.
There's a growing possibility that such paralysis will be broken only by catastrophe.
Statements from senior aides indicate that outcome is a growing possibility.
Social upheaval appears to be a growing possibility, with poverty and corruption pushing people toward Islamic fundamentalism.
Mr. Greenspan said that stagflation — when inflation accelerates and the economy weakens — is a growing possibility, given last week's data showing spiking consumer prices.
With Mr. Putin giving Russian foreign policy a more nationalist edge, there is already a growing possibility that relations between Moscow and Washington will become more quarrelsome.
As we report (see article), there is no chance that the government can defeat the rebels; there is, however, a small but growing possibility that the rebels could defeat the government.If this were purely an internal matter, the world could afford to look shamefacedly away.
The Federal Reserve cut its benchmark interest rate by half a percentage point for the second time this month, making clear that it intends to wage an aggressive battle against the growing possibility of a recession.
The Federal Reserve today cut its benchmark interest rate by half a percentage point for the second time this month, making clear that it intends to wage an aggressive battle against the growing possibility of a recession.
At issue this time, however, are two factors that were not in play after the 2009-10 season: Rivers will be a free agent, and there is the growing possibility of a lockout starting July 1 that could threaten the 2011-12 season.
On Tuesday, Piers Morgan opened his show with an in-depth panel discussion on the growing possibility of a war between Syria and the U.S. that included an intelligent debate about the legal justification for such action.
