Van Persie has been linked with a move away from the Emirates Stadium as he has just 12 months left to run on his current contract.
Arsene Wenger does not want to see his skipper and star striker depart, but the club risk Van Persie leaving for nothing when his deal expires next summer if he does not agree a new one in the meantime.
Manchester City have been strongly linked with a move for the Holland international, while Real Madrid and Barcelona have been mooted as other possible destinations.
Arsenal chief executive Ivan Gazidis confirmed discussions had taken place at the end of the season and insisted the north London club would not be rushed into making any announcement on Van Persie's future.
Now the striker's father, Bob, has ruled out the possibility of a switch to the Etihad and also moved to quell suggestions his son could move to Spain.
"He'd never go to Manchester City as it's impossible he would play for another Premier League side that wasn't Arsenal," Bob van Persie is quoted as saying by El Mundo Deportivo.
"It would make no sense to go to Barcelona when they've already got Leo Messi.
"Real Madrid would be a good option, but they are not so much a team as a collection of star names, so he wouldn't really fit in there either."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
Ajax has released their away soccer jersey for the 2013/14 season. Get in the Gear.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.