But whether Fox realises that dream will depend on the NZOC's attitude, and if he still gains the nod ahead of Hendry who also finished fourth in a tournament in the United States which also counted towards world ranking points.
NZOC spokesperson Ashley Abbott today confirmed there was no certainty that New Zealand would send a second male golfer to Rio beyond Lee.
Athletes need to meet international standards, she said.
The NZOC will discuss its selection criteria with NZ Golf by the July 18 cutoff date for Rio selection.
"Generally they point towards an athlete being able to demonstrate they can finish in the top 16 with the potential to finish in the top eight," Abbott said.
"It is still undecided. The process is not complete. We have tough criteria and there are several steps to go."
Fox admitted trying to secure an Olympic berth weighed heavily on his mind during his final round in Slovakia.
"Early on, I struggled with it a bit - it was a bit stressful," he conceded, revealing he struggled with his putter before an eagle on the 14th changed his mindset from trying to qualify to actually having a crack at winning the tournament.
Although other top golfers have shown an indifferent attitude towards Rio with some of the world's best pulling out, Fox admitted he is hoping he can get to Rio.
"Obviously it's a pinnacle event worldwide," said. "I know golf hasn't quite treated it like that as such but I can't turn down that opportunity (even) with the worries everybody has about Rio."