According to the BBC, police were called out to deal with a row on Friday believed to be between the cricketer and his ex-wife and her new partner.
Surrey Police said they were called to deal with a "domestic dispute" at a house in Epsom in southern England.
They added no-one had been arrested but an allegation of common assault was made and was being investigated.
Thorpe, 34, who last week returned from England's tour of Sri Lanka, has had a widely-publicised separation from his former wife Nicola who lives at the house with the couple's two children.
"Surrey Police were called to a domestic dispute at the house in Epsom at about lunchtime on December 26. An allegation of common assault was made which is being investigated. No-one has been arrested," a spokesman for Surrey police said on Saturday.
Thorpe returned to the England side for the final Test against South Africa in September and scored 124.
He had opted out of all cricket following the second Test against India at Lord's in July 2002 as his marriage collapsed and the player told the selectors he was ready to tour Australia only to change his mind.