The Gunners spent most of last summer preoccupied with the contract situations of Mesut Ozil and Alexis Sanchez, with only the German signing a new deal as the Chilean joined Manchester United in a straight trade in January.
Now they face the same predicament with Ramsey, with the Welshman only contracted until 2019.
So far talks over an extension have proven unsuccessful despite Ramseys willingness to stay at the Emirates, alerting the likes of Manchester United and Chelsea to his potential availability.
And The Sun report that Arsenal will cash in towards the end of the transfer window if Ramsey looks unlikely to sign a bumper new deal.
The north London club felt they missed out on a sizeable transfer fee when Sanchez left – only getting Henrikh Mkhitaryan in return – while Ozil held them to ransom over a new club-record wage packet.
If Arsenal are unable to agree terms with Ramsey, they will invite offers of £40million for the Welshman – a bargain even if he only has one year to run on his deal.
For his part, Ramsey is happy at the Emirates but – particularly in light of Ozil and Mkhitaryans massive deals – recognises that he could be earning double his £100,000-a-week salary.
Arsenal are reluctant to give in to that wish, with their rocketing wage bill already one of the highest in the Premier League, and they could be forced to cash in on Ramsey.
More: Arsenal FC