The phrase "a potential run for" is correct and usable in written English.
It can be used when discussing someone's possible candidacy for a position, typically in politics or sports.
Example: "She is considering a potential run for the mayoral office in the upcoming election."
Alternatives: "a possible candidacy for" or "a prospective bid for".
He will concentrate on a potential run for president.
The effort came as Mr. Giuliani lays the groundwork for a potential run for governor in 2010.
49 is entirely focused on its political role in creating a statewide campaign vehicle for Schwarzenegger, a precursor to what was then only a potential run for governor.
Kerry insisted he's focused on helping other Democrats such as Olive win in 2006, and not on a potential run for president in 2008.
With the comments, Mrs. Clinton was widely interpreted to be distancing herself from Mr. Obama before a potential run for president in 2016.
The trip has raised speculation she is honing her foreign policy credentials before a potential run for the US presidency next year.
An interview on March 25 with Sandra Lee, the cookbook author and girlfriend of Gov. Andrew Cuomo, referred imprecisely to the presidency of Chester A. Arthur, in relation to a potential run by Cuomo for the office.
"Early next year, he'll be stepping down to pursue exploratory efforts for a potential run in 2004," said Rachel Noerdlinger, spokeswoman for his group the National Action Network, which is based in Harlem.
Woods said he spoke to Schumer briefly about a potential run at a memorial service for McCain in Washington last week.
The signs of Clinton's impending presidential run were, literally, everywhere, courtesy of Ready for Hillary, the Super Pac that has been preparing the ground for a potential run.
But come April, the Warriors are likely to be out of the Western Conference playoff race and headed toward the draft lottery, and the Pistons should be gearing for a potential run toward the finals.
