The 19-year-old has been one of the standout stories of the Premier League season since joining from Vasco da Gama in January, with Bournemouth paying around €35m, equivalent to roughly £30m, to complete the deal.
Rayan has scored five goals and provided two assists in 14 Premier League appearances, his pace, dribbling and aggression in one-on-one situations quickly establishing him as one of Bournemouth's most influential attacking players.
That form earned him a place in Carlo Ancelotti's Brazil squad for the World Cup, a remarkable achievement for a player who only turned 19 earlier this year and had been playing in Brazilian football just months earlier.
According to RTI Esporte in Brazil, Liverpool are watching the player as a possible long-term alternative to Mohamed Salah, with the report suggesting Rayan is among the names being considered as part of the club's forward planning.
The connection carries added significance because of Andoni Iraola's recent arrival at Liverpool. The Spanish coach worked with Rayan during his time at Bournemouth and is said to know the player's qualities in detail, particularly his speed, dribbling ability and intensity in individual duels.
RTI Esporte report that Iraola's familiarity with Rayan could prove important if Liverpool decide to move beyond monitoring and into formal interest, given the head coach's first-hand experience of how the winger has adapted to English football.
There is no official offer for Rayan at this stage, and Bournemouth would be under no pressure to sell a player who has rapidly become central to their attacking play. However, the report notes that even the possibility of a move to Anfield is being followed closely in Brazil, largely because of the financial implications for Vasco da Gama.
Vasco are monitoring the situation closely due to the FIFA solidarity mechanism, which entitles clubs involved in a player's development to a share of future transfer fees. Typically, 5% of a transfer's total value is distributed among the clubs that contributed to a player's formation, with the exact amount for Vasco depending on the length of time Rayan spent registered with the club as a youth player.
Any significant sale by Bournemouth would therefore generate a payment for the Rio de Janeiro club, even without Vasco being directly involved in negotiations. For now, Rayan's focus remains on Bournemouth and Brazil's World Cup campaign, but the interest from Anfield adds another layer to a remarkable first six months in European football for the teenager.