Ramsey has just over 12 months remaining on his existing deal at the Emirates Stadium and should fresh terms not be penned, Arsenal will expect offers for the player's signature before the start of next season.
The situation potentially leaves the Gunners to make a decision over whether to sell Ramsey or run the risk of a free transfer in 2019 but according to The Sun, the club have no plans to not receive a fee for the Wales international.
Arsenal took the same risk on Mesut Ozil and Alexis Sanchez last summer, with Ozil eventually penning a lucrative new contract and Sanchez being used in a direct swap with Manchester United's Henrikh Mkhitaryan.
The report suggests that while negotiations have been held with Ramsey, little progress has been made and it may take significant developments over the coming weeks for Arsenal not to invite offers in the region of £40m.
Ramsey has been with Arsenal since 2008, scoring 58 goals in 327 matches in all competitions.