It follows the emergence of photographs which appear to show the art collector with his hand around Lawson's neck as the pair sat on the terrace of a restaurant.
Lawson, 53, the daughter of former chancellor Lord Lawson, was reportedly seen weeping following the episode outside Scott's in Mayfair, central London.
The couple have declined to comment about newspaper reports they had an argument outside the restaurant.
Both are said to be regular visitors to the upmarket restaurant, in Mount Street.
Scotland Yard said it was aware of the photographs which appeared in the Sunday People newspaper. A spokesman said: "Inquiries are in hand to establish the facts of the incident."
He added that Lawson had not made any complaint to the police. Lawson wed Saatchi, 70, who made his name in advertising, in 2003.
She has two children, Cosima and Bruno, from her marriage to journalist John Diamond, who died of throat cancer in 2001.
She became a household name in 1998 with her first cookery book, How To Eat.