The Dutchman plundered 30 Barclays Premier League goals to help fire Arsenal to a third place finish, ending what had been a testing campaign on a high with Champions League football secure once again. The 28-year-old still has 12 months left on his current deal, but so far talks over what is understood to be a lucrative extension have yet to be concluded.
With the likes of Manchester City and new Italian champions Juventus ready to offer big money to lure him away from Emirates Stadium, former Arsenal defender Keown said: "We need to give Robin time and not suffocate him."
He added: "Robin understands and we all understand he is very much a special player for Arsenal. The adulation and respect which he has at Arsenal, Robin has worked a footballing lifetime to get that.
"If he leaves, he might find it hard to grow into another club with the respect he has here.
"However, he might feel he wants to go to a club where he thinks he can win things - that is probably the dilemma for him, rather than the financial one.
"It is swapping the love for him here if he goes to another club, he might find it a little bit of a difficult transition which he does not want to make."
Arsenal overcame an appalling start which saw them lose four from the opening seven league games to overhaul rivals Tottenham into third place.
Keown feels should Arsene Wenger's men be able to recapture the form of the latter part of the campaign, then 2012/2013 could yet turn out to be a vintage campaign.
He said: "It ended up as a dream finish for Arsenal, because at the start of the season, it was a bit of a nightmare in terms of results. Arsene Wenger will now look to improve things for next season, when it will just be about consistency."