The 50-year-old has been asked to attend after allegedly calling a man of Indian heritage a “waste of a white man’s skin” in a series of WhatsApp exchanges.
In other WhatsApp messages, Baroness Mone allegedly described the man’s partner as “a mental loony” and “nut case bird”.
She has denied the claims, which were first reported last month following complaints to the House of Lords Commissioner for Standards.
The Sun has since reported that Lady Mone, who has not been arrested, has been asked to attend a police station for interview under caution.
A Met spokesman said: “In June, police received an allegation of a racially aggravated malicious communication in relation to information posted on a messaging app.
“Police spoke to the complainant and advised that for the investigation to progress a statement would need to be taken; for this to be admissible in any future court proceedings, this would need to be done in person.
“In October, the complainant gave a statement to police and the investigation continues.
“A 50-year-old woman has been invited to attend for an interview under caution at a future date.”
The incident was reported in December after a man had complained to the House of Lords Commissioner for Standards regarding the messages.
Its officers said they were unable to investigate because the exchange was not in the course of Baroness Mone’s parliamentary duties.
At the time, a statement said: “Baroness Mone is 100 per cent not a racist. Baroness Mone and her husband have built over 15 schools in Africa in the past three years.”
Her lawyers later said Baroness Mone had “no access” to the messages and no “detailed memory of them”.
They added: “She is not prepared to comment on the messages unless and until their authenticity has been confirmed.
“But Baroness Mone, in any event, very strongly denies that she is a racist, a sexist or that she has a lack of respect for those persons genuinely suffering with mental health difficulties.”