Police have warned Heather Mills-McCartney over a "non-specific threat" made to her safety.
Heather Mills McCartney has spoken of receiving death threats
Sussex Police said they had spoken to the estranged wife of Sir Paul McCartney about the threats, uncovered by officers in Merseyside.
Lady McCartney, 38, recently spoke of receiving death threats following her separation from the former Beatle.
Police said there was no "imminent risk". They had also spoken to Sir Paul, they said.
Sir Paul, 64, announced his split from the former model in May. The couple had been married four years and have a three-year-old daughter, Beatrice.
Bernie Murphy, Sussex Police Force Command and Control Centre supervisor, based in Brighton, said that on receiving the information the threat was risk-assessed.
"Police can confirm that Mills McCartney was spoken to by officers and was fully informed of all the information, including details of the names of individuals involved.
"In addition, Mills-McCartney's estranged husband was also spoken to.
"Local officers have been fully briefed regarding the circumstances and provision has been made for an immediate police response should this be necessary."
Mr Murphy added that it was possible that an alarm had been installed in her Hove home.
Lady McCartney told the BBC earlier this month that she had recently received death threats and that the "very scary" situation had caused her severe depression.