Scott, who has two years remaining on his contract, is also attracting serious attention from Manchester City, Manchester United, Tottenham Hotspur and Chelsea, but Bournemouth are focused on extending his deal rather than entertaining any offers.
The former Bristol City player earned his first England call-up last November and was subsequently included in Thomas Tuchel's extended pre-World Cup training camp in Florida, though he did not appear.
Arsenal's need for a central midfielder has also led them to explore moves for Newcastle United pair Bruno Guimarães and Sandro Tonali. A move for Guimarães is currently considered more realistic, with Tonali's price believed to be a stumbling block.
Bournemouth's refusal to engage on Scott signals a clear intent to build around one of their most valuable assets. The volume of interest — six clubs in total — reflects how highly regarded Scott has become and makes the contract extension talks all the more pressing for the south coast club.
Scott's omission from the final World Cup squad — despite being involved in pre-tournament preparations — has not dampened interest from the top clubs, and his performances for Bournemouth last season clearly left a strong enough impression to generate a queue of suitors at the start of the summer window.
For Arsenal, the rejection narrows their options in central midfield and increases the pressure to find a workable route to either Guimarães or Tonali, both of which come with their own significant obstacles. Scott's unavailability removes what might have been a more straightforward — if still expensive — solution to their midfield needs.
Bournemouth's position is firm for now, but with so many clubs circling and a contract that has two years to run, the club will need to move quickly on an extension if they are to avoid a repeat of this situation next summer.