The 22-year-old has been a key player for his La Liga club during the 2022-23 campaign, featuring on 22 occasions in all competitions, contributing three goals and five assists in the process.
Henrique scored twice and registered two assists in six appearances in the group stage of this season's Europa League, while he has one goal and one assist in 14 league appearances.
The Brazilian also starred for Real Betis in the semi-finals of the Spanish Super Cup against Barcelona on Thursday night, providing two assists in a 2-2 draw, before Manuel Pellegrini's side lost on penalties.
According to ABC Sevilla, both Arsenal and Man United have been monitoring the attacker's performances during the 2022-23 campaign.
The report claims that the two Premier League clubs have sent scouts to watch Henrique in action this season, but a move during the January transfer window is seen as highly unlikely.
Henrique came through the youth system at Fluminense and went on to make 118 appearances for their first team, scoring 14 goals and registering 13 assists in the process.
The attacker has only been with Real Betis since last summer, and he has a contract in Seville until June 2028, placing Pellegrini's side in a strong position to keep hold of him.
Henrique is capable of playing in a number of different positions in the final third of the field, but he has largely operated off the right for his La Liga club this season.
Arsenal had thought to be closing in on a deal for Mykhaylo Mudryk, but Chelsea have won the race to sign the Ukraine international from Shakhtar Donetsk.
As a result, the Gunners have been forced to move their attention away from the 22-year-old, as head coach Mikel Arteta looks to boost his attacking options this month.
Man United, meanwhile, will be in the market for a new centre-forward during this summer's transfer window, having terminated Cristiano Ronaldo's contract at the end of November.
Henrique's ability to play in a number of different positions is said to appeal to both Premier League clubs, but he will now be worth substantially more than the £7m that Real Betis paid for his signature last summer.
The forward is expected to next be in action in his side's Copa del Rey last-16 contest with Osasuna on Wednesday night.