Van Persie announced that he would not be renewing his contract at the Emirates Stadium, which expires next summer, on Wednesday, with Manchester City, Manchester United and Paris Saint-Germain understood to be admirers of the prolific Dutchman.
And Parlour, who enjoyed a distinguished 12-year spell with the north London club, believes Arsenal should cash in on their star man then set their sights on acquiring a replacement.
"What Arsenal have got to do now is try and get the best bidder," Parlour told talkSPORT.
"£25 million or £30m, get as much money as you can and then reinvest the money in the squad.
|VAN PERSIE TO PARIS?
|18/1||PSG are 18/1 to be Robin van Persie's next permanent club with Paddy Power|
"Let's go out and make a key signing like Papiss Cisse from Newcastle and suddenly people will forget about Robin van Persie."
The Gunners have already brought in forwards Lukas Podolski and Olivier Giroud this summer, and reports have strongly linked them with a move for Rennes midfielder Yann M'Vila.
Wenger had insisted before Van Persie's announcement that the captain must be retained next season "at all costs".