The 29-year-old's future has been the subject of intense speculation this summer, with champions Manchester City and Italian club Juventus both reported to be keen.
City's neighbours Manchester United are thought to be leading the race for the Dutchman's signature, however, with Van Persie announcing that he does not plan to extend his contract at the end of the season.
|11/2||Arsenal are 11/2 with Bet365 to be the Premier League's highest-scoring team this season
"To me he looks fit and sharp in training," he told Sky Sports. "He's working hard. He's working on his fitness. I don't see anything different and I hope he stays the next four years as well."
Van Persie was given just 20 minutes to impress in Arsenal's 4-0 pre-season win against FC Koln on Sunday and Vermaelen remained coy when asked about his team-mate's future.
"I've no idea," he added. "I hope [he stays]. I don't know what happens behind the scenes but at the moment I can only say he's a player for Arsenal."
Arsene Wenger has added German international Lukas Podolski as well as Olivier Giroud and Santi Cazorla to his squad as the Gunners look to end their seven-year trophy drought and the Belgium defender is confident that they can compete ahead of Saturday's curtain raiser against Sunderland.
"I feel really positive for the new season," he insisted. "If we all stay fit, the squad is strong enough to compete for the title."