The Sun says the Gunners have still not made any progress with Ramsey's new contract sparking fears over his future.
The Welsh midfielder has just 11 months left on his deal, and can start speaking to others clubs in January.
It is understood talks began over fresh terms as far back as last year, but there has been little movement since.
A source said: “Arsenal need to make their move soon and are being slow to the punch as usual.
“They could lose another one of their top stars if they are not careful. It's a very delicate situation."