The Gunners are open to the possibility of loaning out the English goalkeeper for one season, with an option to buy included in the deal.
Per Evening Standard, Arsenal had initially preferred to sell Ramsdale this summer.
But they are willing to compromise, as they know that he wants to play regularly.
Bournemouth are also interested in pursuing a loan deal for Ramsdale, given they want a new goalkeeper.
However, they are not willing to put up the money to sign him permanently either.