Around 2,300 BBC roles will relocate to the BBC North base, including parts of the future media and technology, children's, learning, Radio 5 Live and marketing teams.
According to The Guardian, the BBC has confirmed that Van Klaveren will rent a flat for two years close to Salford Quays under the corporation's relocation programme, paid for by the licence fee.
A BBC spokesman said that Van Klaveren has opted against a permanent relocation as he does not want to disrupt his children's education, which is at a critical stage.
After the two-year period in rented accommodation has been completed, the spokesman said that Van Klaveren will "review the situation and make arrangements at his own cost".
The development follows news this week that Peter Salmon, director of the BBC North facility at Salford Quays, will also not be moving his family north in the foreseeable future.
Salmon's wife, former Coronation Street actress Sarah Lancashire, is understood to have told friends that she is staying at the family home in Twickenham.
In a further blow to the relocation plans, the BBC said yesterday that BBC North chief operating officer Richard Deverell "still hasn't made a decision" on whether to move from Surrey with his wife and children.
Earlier in the month, the BBC confirmed plans to relocate BBC Breakfast to Salford Quays in a move that has reportedly angered staff on the morning programme.