The phrase "arguably around" is correct and usable in written English.
It can be used when discussing a point that is open to interpretation or debate, often to indicate an approximate figure or situation.
Example: "The population of the city is arguably around one million, though estimates vary."
Alternatives: "possibly about" or "potentially around".
When Lil Wayne peaked, arguably around 2008, he was lauded as a hip-hop outsider bolstering a genre that had become stuck on the sort of aspirational sheen which made names of rappers such as P Diddy and Jay Z.
Moreover, it was the administrative machinery of the welfare state, developed (arguably) around the problems of modernity, that produced the vast aggregations of personal data, in doctors' records and insurance returns, that served as indices of the nation's psychological health.
Netanyahu has arguably poked around in American domestic politics more conspicuously than any foreign leader in memory, using his influence in Washington to bolster lobbying and campaign-finance groups that mainly support Republican candidates.
Franklin D. Roosevelt arguably turned around the mood of a country that appreciated his buoyant style, reassuring fireside chats and certitude that the only thing to fear was "fear itself," even as the Great Depression raged on for years.
That article was written in context of the wider troubles afflicting country and cricket, to explain how Pakistan had managed to turn things around in arguably their darkest moments.
These arguably could be turned around.
When healthy, the 10th-year veteran is arguably the best all-around receiver in football.
Chris Clemons once again looked like arguably the best all-around defensive end in the N.F.C.
One final note: Seattle's Chris Clemons has been arguably the best all-around defensive end in the N.F.C. this season.
Through three weeks, Jennings has been arguably the best all-around cornerback in the N.F.C. (not named Patrick Peterson, that is).
Miller is arguably the best all-around linebacker in the league and perhaps one of the three or four best pass rushers in the N.F.L., too.
