Gossip site TMZ claims the singer has welcomed a boy with a first name that begins with the letter R.
Rihanna is yet to comment on the claims.
The two artists already have a son named RZA Athelston who was born in May 2022. The unusual name is a tribute to rapper RZA, 54, leader of the Wu-Tang Clan.
Rihanna surprised the world by confirming she was pregnant at her halftime Superbowl performance in February.
She was last seen in public at the end of July at a date-night dinner at Italian restaurant Giorgio Baldi in Santa Monica, California.
Rihanna’s rep has been approached for comment.
The couple have known each other for years, but are said to have begun dating in 2020.
Speaking to British Vogue earlier this year, Rihanna reflected on how her relationship with A$AP Rocky has developed since welcoming their son in May 2022, saying: “We’re best friends with a baby… We have to be on the same page, but we’ve always kind of had that in our relationship.
“Everything changes when you have a baby but I wouldn’t say it’s done anything but made us closer.”
On witnessing A$AP Rocky’s connection with their son, she said: “The second Rocky makes eye contact with him he is on fire.
“The whole thing they say about sons and moms, it’s a myth. Sons and fathers is crazy.
“I realised that the validation that you really need as a boy is from your father.”