Arsenal officials have made direct contact with Hinshelwood's representatives and are preparing an official bid, with manager Mikel Arteta viewing the 21-year-old as a strong fit for a squad built around versatile players.
Hinshelwood can operate in central midfield, in a holding role, or at either full-back, a range of positions that has made him a priority target.
Manchester United have also made official inquiries over his availability and are planning a fresh move in the coming days, while Manchester City are understood to be considering a move of their own for the England Under-21 international.
The Sun reports City and Arsenal have both tracked Hinshelwood's progress for much of the past year, with interest first surfacing publicly back in February as Rodri's own future at the Etihad Stadium came under scrutiny and City began weighing up their midfield options for the summer.
A positive scouting report is expected to prompt informal talks with Brighton over terms, with a bid in the region of £43m to £51m thought sufficient to reach an agreement, though the Seagulls would prefer to keep hold of their academy graduate given his importance to Fabian Hürzeler's system.
Hinshelwood, the son of former Brighton player Adam Hinshelwood, still has three years remaining on his contract, giving the south-coast club a strong negotiating position regardless of the level of interest.
He has made 79 senior appearances since breaking into Brighton's first team in 2023, establishing himself as one of the club's most versatile and reliable performers. Comparisons to former Liverpool midfielder James Milner have followed him throughout his rise, largely because of his ability to play across midfield and both full-back positions without any noticeable drop-off in quality, a trait that has made him a target for clubs looking for tactical flexibility as much as raw talent.
Brighton's recent history of developing and selling academy graduates for significant fees, including Moisés Caicedo and Marc Cucurella, means any negotiation is likely to be protracted rather than swiftly concluded.