Bournemouth rejected the request from Arsenal for Alex Scott and they say the midfielder is not for sale this summer.
The Premier League champions are keen to sign a new central midfielder and the 22-year-old is said to be one of their targets.
Scott is also attracting serious interest from other Premier League clubs including Manchester City, Manchester United, Tottenham and Chelsea.
But Bournemouth have signaled their intention to retain the former Bristol City man and are seeking to agree an extension to his current contract, which has two years left to run.
Scott was selected for his first England squad last November and was then called up to Thomas Tuchel’s extended World Cup training camp in Florida, although he never made an appearance.
Arsenal are also considering signing Newcastle pair Bruno Guimarães and Sandro Tonali in their search for a new midfielder.
A move to Guimarães is currently seen as more likely, with Tonali’s price considered a stumbling block.
North London rivals Tottenham are progressing in their efforts to land Tonali and confidence is growing that he can secure a move for the Italian midfielder.
Arsenal are also keeping an eye on West Ham players Matheus Fernandes and Lille’s Ayoub Bouaddi.