Mark Thatcher was "planning to leave" South Africa before his arrest, authorities in the country say.
Sir Mark returned to his home after his Cape Town court appearance
Police say there is "credible evidence" Sir Mark, who is under house arrest, helped finance an alleged coup plot in Equatorial Guinea.
Makhosini Nkosi, National Prosecuting Authority spokesman, said Sir Mark's house was on the market.
Sir Mark, son of former UK Prime Minister Margaret Thatcher, says he is innocent of all charges.
The family's spokesman said Lady Thatcher was "distressed" over Sir Mark's arrest.
"She is obviously distressed about the fact her son appears to be in some difficulty," Lord Bell told Channel Four news.
"(But) she is very confident about the South African legal process and she is sure he will be cleared and named innocent at the end of it."
Appearing in court on Wednesday, Sir Mark was bailed to reappear on 25 November and ordered to pay a two million Rand (£165,000) bail bond.
He is accused of violating laws banning South African residents from taking part in foreign military action.
Sir Mark was arrested on Wednesday at his home in the Cape Town suburb of Constantia.
Sipho Ngwema, a spokesman for the South African police anti-fraud unit known as the Scorpions, said Sir Mark was "planning to leave the country for good" and had enrolled his children in American schools.
And Makhosini Nkosi, a spokesman for the National Prosecuting Authority, said: "It does appear that he was planning to leave the country.
"The house was on the market, he had disposed of some of the cars, and there were suitcases around the house which indicated they were planning to leave.
"He did confirm he was planning to relocate to Texas."
Lord Bell said Sir Mark had no plans to leave South Africa and was merely planning to move to a different suburb of Cape Town.
One of Sir Mark's legal team, Phillip Higgo, said he had been aware of the investigation before returning to South Africa from a US business trip.
Sir Mark, whose wife is from Texas, moved to Cape Town from the United States in the late 1990s but frequently travels between the two.
Investigators were said to be examining his records and computers for information about the alleged plot.
Mr Ngwema told the BBC that police had "credible evidence" of Sir Mark's involvement.
"We allege he is one of the financiers of the coup to overthrow the government of Equatorial Guinea and we have received credible evidence that he has assisted financially in that regard," he said.
"Anyone who is using this country as a springboard for violence and disorder, we are going to deal with those persons quite strongly," he added.
The act specified a fine or imprisonment for conviction, but not the severity, which is left up to the presiding officer, Mr Ngwema said.
Sir Mark said in a statement: "I am innocent of all charges made against me. I have been and am cooperating fully with the authorities in order to resolve the matter.
"I have no involvement in an alleged coup in Equatorial Guinea and I reject all suggestions to the contrary."
Speaking outside the court, Sir Mark's lawyer, Peter Hodes, said he had been held on suspicion of providing financing for a helicopter linked to the coup plot, and intended to plead not guilty.
The alleged plot to overthrow the president of Equatorial Guinea has sparked dozens of arrests across Africa.
The alleged plot leader, former British SAS captain Simon Mann, an old Etonian turned leading African mercenary, has admitted trying to procure dangerous weapons - a charge which carries a possible 10-year jail sentence.