Manchester City lead the chase for the Gunners skipper.
But mother Jose said: “Arsenal love him and that’s a great incentive to stay. Arsenal are a fantastic club.
“They have no debts and Robin is idolised there.”
Spanish giants Barcelona and Italian champions Juventus also want to sign Arsenal’s double Footballer of the Year.
RVP opened negotiations with Arsene Wenger and chief executive Ivan Gazidis in London last week.
The Gunners are offering him a new £130,000-a-week deal, plus a £5million re-signing bonus to enhance his position as the club’s highest-paid player.
Van Persie’s wife Bouchra added: “Arsenal showed faith in Robin when he was going through a lean time, so we should not repay them by thinking about other clubs.
“Our home life and our children are happy in London.”